LIGHT
(1) LIGHT, ITS RECTILINEAR PROPAGATION, SHADOWS
=352. A Comparison of Sound and Light.=--Light from the standpoint of
physics is considered much as is _sound_, as a _mode_ of _motion_; one
affecting the ear, the other producing the result called _vision_. There
are other differences also worth considering. (a) While sound travels as
vibrations of some _material_ medium, light travels only as vibrations
of the _ether_; solids, liquids, and gases act so as to hinder rather
than to assist in its movement. That is, light travels best in a vacuum
or in a space devoid of ordinary matter. (b) The _speed_ of light is so
great that at ordinary distances on the earth its motion is practically
instantaneous. Experiments have shown that its speed is about 186,000
miles to 300,000 kilometers a second.
=353. Luminous and Illuminated Bodies.=--If we consider the objects
within a room, some of them, as books and furniture, would be invisible
if all light from external sources were excluded. On the other hand,
some other objects, such as a lighted lamp, a burning coal, or a red hot
iron, would be seen if no outside light were present. Such bodies are
said to be luminous. Most luminous bodies are hot and become
non-luminous on cooling. There are, however, some bodies that are
luminous at ordinary room temperatures, as the firefly and some
phosphorescent paints. When light emitted by a luminous body strikes an
object, a portion of it is always _reflected_. It is this reflected
light that makes the illuminated object _visible_. If the object is a
sheet of glass, some of the light is _transmitted_. If a substance is so
clear that objects can be seen through it, the substance is
_transparent_, but if objects cannot be seen through it, the substance
is said to be _translucent_. Objects transmitting no light are _opaque_.
Some of the light falling upon a body is neither reflected nor
transmitted, but is _absorbed_ and tends to warm the body. The light
falling upon a body is therefore either _reflected_, _transmitted_, or
_absorbed_. Thus Fig. 345 represents light coming from _S_ to a piece of
glass _GL_. A portion of the light represented by _R_ is reflected.
Another part _A_ is absorbed and disappears, while still another part
_T_ is transmitted and passes on.
[Illustration: FIG. 345.--The light is transmitted (_T_), reflected
(_R_), or absorbed (_A_).]
There is no sharply drawn line between transparent and opaque bodies.
Very thin sheets of gold transmit a greenish light, and experiments have
shown that substances as transparent as clear water absorb enough light
so that at considerable depths in an ocean or lake little or no light is
ever found. All light whether from luminous bodies or reflected from
non-luminous objects shows certain properties which will now be
considered.
=354. The Rectilinear Propagation of Light.=--If a beam of light passes
through a hole in a window shade into a darkened room, it is seen to
follow a perfectly straight course. If a person while coughing holds a
book before the face, the sound passes around the book and is heard at
any point in the room while the face is hidden by the book. In other
words, light ordinarily does not pass around corners as sound does, but
travels in _straight lines_. This fact is made use of when one aims a
gun or merely looks at an object. So well established in our minds is
the idea that an _object_ is in the direction from which we see the
light coming to us from it, that we are sometimes deceived as to the
real position of an object, when the course of the light from it has
been changed by a mirror or some other reflecting surface. Many
_illusions_ are produced in this way, of which the _mirage_ of the
desert is one example. (See Art. 381.)
[Illustration: FIG. 346.--Shadow from a small source of light.]
[Illustration: FIG. 347.--Shadow when source of light is large.]
=355. Shadows.=--_A shadow is the space from which light is cut off by
an opaque body._ Thus if a book (see Fig. 346) is held between a screen,
_N_, and a _small_ source of light, _L_, a shadow is produced which
extends from the book to the screen. Notice that the shadow is a _space_
and not an _area_. If a _large_ gas flame (see Fig. 347) is used as the
source of light, the shadow of the book is no longer clear cut at the
edges as before, but has a darker central part with a lighter fringe of
partial shadow at the edges. The dark portion within the shadow has all
the light excluded from it and is called the _umbra_. The lighter
portion of the shadow at the edges has only a part of the light from the
flame cut off. This portion is called the _penumbra_. when one stands in
sunlight his shadow extends from his body to the ground or object on
which the shadow falls. At night we are in the earth's shadow, which
extends out into space beyond the earth.
[Illustration: FIG. 348.--Character of the earth's shadow.]
=356. Eclipses.=--Since the sun is a very large object the shadow cast
by the earth contains both umbra and penumbra. (See Fig. 348.) When the
moon passes into the shadow of the earth, there is said to be an eclipse
of the moon, while if the moon's shadow falls upon the earth, the
portion of the earth cut off from the sun's light has an eclipse of the
sun.
=357. Images by Small Apertures.=--The straight line movement of light
makes possible the _pin-hole_ camera, by which satisfactory photographs
have been made. The action of this device may be illustrated by placing
a luminous body, a lighted candle, an incandescent lamp, or a gas flame,
in front of a piece of cardboard, _S_, which has a small opening in it.
Light from the object (see Fig. 349) falls upon a screen, _S_{2}_, so as
to produce an _inverted image_. Other applications of this principle
will be given later.
In Fig. 349 let _PQ_ represent a gas flame, then light from point
_P_ at the _top_ of the flame will pass in a straight line through
the opening or aperture of the cardboard and strike at _P_{2}_ at
the _bottom_ of the illuminated spot upon the screen. Light from
_Q_ passing in straight lines through the aperture will strike at
_Q_{2}_ at the top of the lighted space. This spot of light will
have the same outlines as the luminous body _PQ_ and being formed
as just described will be _inverted_.
[Illustration: FIG. 349.--Image formed by a small aperture is inverted.]
This spot of light, resembling in its outlines the flame, is called an
_image_. _An image is defined as an optical counterpart of an object_.
Images are formed in a variety of devices, such as _apertures_,
_mirrors_, and _lenses_. The _pin-hole camera_ is simply a light-tight
box with a small aperture in one side. Light passing through this
aperture forms an image upon the opposite side of the interior of the
box, of whatever object is in front of the camera. Light entering a room
through a _large_ aperture such as a window produces a multitude of
overlapping images which blend to form a somewhat evenly illuminated
surface.
Important Topics
1. Light contrasted with sound (three differences).
2. Bodies: transparent, translucent, opaque.
3. Light: reflected, transmitted, absorbed.
4. Light travels in straight lines, evidence, shadows, umbra, penumbra.
5. Formation of images by small apertures.
Exercises
1. Consider the circumference of the earth as 25,000 miles. How many
times would the speed of light cover this distance in a second?
2. How soon after any great disturbance takes place on the sun,
93,000,000 miles distant, can it be seen upon the earth?
3. Construct a diagram of the moon's shadow. How much of the sun can one
see when in the moon's umbra? When in its penumbra? Have you ever been
in either? When? Have you ever been in the earth's umbra? In its
penumbra?
4. Explain, using a diagram, the formation of an inverted image by a
small aperture.
5. If the sun is 45 degrees above the horizon, what is the height of a
pole casting a shadow 60 ft. long?
6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically
upon a walk, how tall is the tree whose shadow is 42 ft. long, both
measurements being made at the same time?
7. Why are the shadows caused by an electric arc lamp so sharply
defined?
8. Why should schoolroom windows be all on one side and reach to the
ceiling?
9. What is the relation between the size of an image and its distance
from the aperture forming it? Can you prove this by geometry?
10. What are silhouettes and how are they produced?
(2) PHOTOMETRY AND THE LAW OF REFLECTION
=358. Photometry.=--It is desirable at times to compare the intensities
of illumination produced by light from different sources. This is done
to determine the _relative cost or effectiveness_ of various illuminants
such as candles, kerosene and gas lamps, and electric lights The process
of determining the relative intensity of lights or lamps is called
photometry. (_Photos_ = light.)
The unit for measuring the power of light is called a _candle power_. It
is the light produced by a sperm candle burning 120 grains per hour. An
ordinary gas light burns 5 or more cubic feet of gas per hour and yields
from 15 to 25 candle power. A Welsbach gas lamp, consuming 3 cu. ft. per
hour, produces 50 to 100 candle power.
Instead of using candles, for practical photometry, incandescent lamps
standardized by the Bureau of Standards are used for testing or
calibration purposes.
It is necessary to distinguish between the intensity of a _luminous_
body, _i.e._, as a source of light, and the _intensity_ of
_illumination_ upon some surface produced by a light. It is considered
that two sources of light are of _equal intensity_ if they produce equal
illumination at equal distances.
=359. Law of Intensity of Light.=--A device for measuring the candle
power of a light is called a _photometer_. Its use is based upon the
_law of intensity of light_. _The intensity of illumination of a surface
is inversely proportional to the square of its distance from the source
of light._ This relation is similar to that existing between the
intensity of a sound and the distance from its source. The following
device illustrates the truth of this law in a simple manner.
[Illustration: FIG. 350.--The light spreads over four times the area at
twice the distance.]
Cut a hole 1 in. square in a large sheet of cardboard (_K_) and
place the card in an upright position 1 meter from an arc light or
other _point source_ of light (_L_). Now rule inch squares upon
another card (_M_) and place it parallel to the first card and 2
meters from it. (See Fig. 350.) The light that passed through the
hole of 1 sq. in. at a distance of 1 meter is spread over 4 sq.
in. at a distance of 2 meters. Therefore, the intensity of
illumination on each square inch of _M_ is one-fourth that upon the
surface of _K_. If _M_ is placed 3 meters from the light, 9 sq. in.
are illuminated, or the intensity is one-ninth that at 1 meter
distance.
[Illustration: FIG. 351.--The Bunsen photometer.]
These relations show that the intensity of illumination is inversely
proportional to the square of the distance from the source of light. An
application of the law of intensity is made in using a simple (Bunsen)
photometer. This consists of a card containing a spot soaked with oil or
melted wax. (See Fig. 351.) The lights whose intensities are to be
compared are placed upon opposite sides of the card. The card is then
adjusted so that the spot appears the same on both sides. The
illumination is now equal on both sides of the card and the _candle
powers of the two lights are proportional to the squares of their
distances from the card_. The simple device just described will give
approximate results only. For accurate results more elaborate apparatus
is required.
=360. Measurement of the Intensity of Illumination.=--A standard candle
(Art. 358) produces when lighted 1 candle power. The illumination caused
by this upon a surface 1 ft. away and at right angles to the light rays
is called a =foot-candle=. It is the unit of intensity of illumination.
A 4-candle-power lamp, at a distance of 1 ft., produces 4 foot-candles.
A 16-candle-power lamp at a distance of 2 ft. also produces 4
foot-candles--(16 ÷ 2²).
The intensity of illumination required for a good light for seeing
varies with the conditions. Thus, for stage and store lighting about 4
foot-candles are needed, while homes and churches may require but 1
foot-candle.
Too great an intensity of illumination is as harmful as not enough.
Exposed lights having an intensity of more than 5 candle power per
square inch are often a cause of eye trouble. Such lights should be
protected by frosted globes.
A pleasing form of lighting for large halls and public buildings is the
_indirect system_. In this, the lamps are hidden by reflectors which
throw the light upon the ceiling from which it is diffused over the
room. This form of lighting is more expensive than other systems since
but a part of the light is reflected. Its cost therefore is an important
factor when considering its use.
=361. The Reflection of Light.=--The light reflected from the surfaces
of bodies about us gives us information concerning our surroundings. A
knowledge of the behavior of light undergoing reflection is not usually
gained from ordinary observation. The law of reflection of light may be
shown, however, by an experiment.
[Illustration: FIG. 352.--_B´_ is as far back of the mirror as _B_ is in
front of it.]
[Illustration: CHRISTIAN HUYGENS
(Popular Science Monthly)
Christian Huygens (1629-1695). Dutch physicist; invented the pendulum
clock (1656); developed the wave theory of light; discovered
polarization of light (1690).]
[Illustration: H. V. HELMHOLTZ
"By Permission of the Berlin Photographic Co., New York."
Hermann von Helmholtz (1821-1894) Germany. Established the doctrine of
conservation of energy; made many discoveries in sound; invented the
ophthalmoscope; established the physical basis of tone quality.]
A plane mirror, _M_, is held in a vertical position resting upon a
sheet of paper. (See Fig. 352.) Pins are set upright in the paper
at _A_ and _B_. On placing the eye along the line _AC_ and looking
toward the mirror an image of _B_ may be seen in the mirror due to
the light reflected from its surface. Pins _C_ and _D_ are now set
in the paper so that when one looks along the line _BD_ toward the
mirror one may see all four pins apparently in one line. This
indicates that the light from _A_ and _C_ passing along _CA_ toward
_O_ is reflected back along the light _CBD_. By means of a ruler,
draw lines through _BD_ and _AC_ till they intersect at _O_. Also
draw _PO_ perpendicular to the mirror at _O_.
Then the angles _AOP_ and _BOP_ will be found equal. These are called
the angles of _incidence_ and _reflection_ respectively. _The law of
reflection_ is therefore stated: _The angle of reflection is equal to
the angle of incidence._ These angles are in the same plane, that of the
paper. This law applies in all cases of reflection of light. It is
similar to the law of reflection of sound (Art. 326.)
Important Topics
1. Photometry, law of intensity, candle power, foot-candle.
2. Intensity of illumination.
3. Reflected light and law of reflection.
Exercises
1. Both sides of a card are equally illuminated when two lights are on
opposite sides of it and 10 and 30 cm. respectively from it. what are
their relative intensities?
2. What are the relative intensities of illumination from a gas light
upon a book 6 ft. and 2 ft. respectively from the light?
3. Which is more expensive per candle power? How many times as
expensive? A 50-watt 16-candle-power incandescent lamp at 10 cents per
kilowatt-hour or a 100-candle-power Welsbach light burning 5 cu. ft. of
gas per hour at 80 cents per 1000 cu. ft. of gas. (Find cost of each per
hour, and then the cost of 1 candle power hour for each.)
4. Why are not ordinary shadows perfectly dark?
5. At what distance will a 16-candle-power lamp give the same
illumination as a single candle at 10 in.?
6. If the sun is at an elevation of 30 degrees what is the angle of
incidence at which it strikes the surface of water? What is the angle
between the incident and the reflected rays?
7. What is the difference between the phenomena of reflection of light
from a white sheet of writing paper and from a piece of clear window
glass?
8. A horizontal ray of light, traveling due east, strikes a vertical
mirror so that after reflection it is traveling due north. If the mirror
be now turned 10 degrees about a vertical axis, the north edge moving
east, what will be the direction of the reflected ray?
9. The necessary illumination for reading is about 2 foot-candles. How
far away may an 8-candle-power lamp be placed?
10. What is the illumination in foot-candles upon a surface 20 ft. from
an arc lamp having an intensity of 1000 candle power?
11. How far from a 100-candle-power Welsbach light would the
illumination be 2 foot-candles?
(3) MIRRORS AND THE FORMATION OF IMAGES
[Illustration: FIG. 353.--Reflection of light, (_a_) diffused, (_b_)
regular.]
=362. Mirrors.=--The many purposes served by mirrors in our every-day
life has made their use familiar to everyone. Yet without study and
experiment few understand their properties and action. _Any smooth_
surface may serve as a mirror, as that of glass, water, polished wood,
or metal. Most objects, unlike mirrors, have irregular surfaces; these
scatter or diffuse the light that falls upon them. (See Fig. 353_a_.)
This is called _diffused or irregular reflection_. The reflection of
light from the smooth surface of a mirror is _regular_. (See Fig.
353_b_.) In every case of reflected light, however, the angle of
reflection equals the angle of incidence, diffusion being due to the
irregularity of the surface. It is by means of the light "diffused"
from the surface of illuminated bodies, such as plants, animals, food,
and manufactured articles, that we "see" the various objects about us,
and it is this light that enables us to judge of their distance, size,
form, color, etc. The moon is seen by the sunlight reflected from its
surface. Moonlight is therefore sunlight diffused by reflection. The
_new moon_ is that phase or condition of the moon when only a narrow
strip of the moon's illuminated surface is turned toward the earth. At
the time of the _full moon_ the whole illuminated surface is seen.
=363. Images Formed by a Plane Mirror.=--The most common use of mirrors
is in the formation of images. The way in which images are formed by a
plane mirror may be illustrated by diagrams. Thus in Fig. 354, let _L_
represent a luminous body and _E_ and _E´_ two positions of the
observer's eye. Take any line or ray as _LO_ along which the light from
_L_ strikes the mirror _O-O´_. It will be reflected so that angle _LOP_
equals angle _POE_. Similarly with any other ray, as _LO´_, the
reflected ray _O´E´_ has a direction such as that angle _L´O´E´_ equals
angle _P´O´E´_. Any other rays will be reflected in a similar manner,
each of the reflected rays appearing to the eye to come from a point
_L´_ behind the mirror.
[Illustration: FIG. 354.--The virtual image of a fixed object as seen in
a plane mirror, has the same location from every position of the
observer's eye.]
=364. Light Waves and Wave Diagrams.=--Just as a stick continually moved
at the surface of a body of water sets up a series of waves spreading in
all directions, so one may imagine a train of waves sent out by a
luminous body _L_ (as in Fig. 355) to the mirror _MN_. These waves will
be reflected from the mirror as if the source of light were at _L´_. It
is much simpler and more convenient to locate the position of the image
of a point by the use of lines or "rays" (as in Fig. 354) than by the
wave diagram (as in Fig. 355). In all _ray diagrams_, however, it should
be kept in mind that the _so-called_ ray is a symbol used to represent
the direction taken by a part of a light wave. Thus in Fig. 354, the
light from _L_ moving toward _O_ is reflected to _E_ along the line
_OE_, the heavy lines representing rays.
[Illustration: FIG. 355.--Wave diagram of image formed in a plane
mirror.]
=365. To locate the image of an object formed by a plane mirror=
_requires_ simply an application of the law of reflection. Thus in Fig.
356 let _AB_ represent an object and _MN_ a plane mirror. Let _AA´_ be a
ray from _A_ striking the mirror _perpendicularly_. It is therefore
reflected back along the same line toward _A_. Let _AO_ represent any
other ray from _A_. It will be reflected along _OE_ so that angle _r_
equals _i_. The intersection of _AC_ and _OE_ at _A´_ behind the mirror
locates the image of the point _A_, as seen by reflection from the
mirror. The triangles _ACO_ and _A´CO_ may be proved equal by geometry.
Therefore _A´C_ equals _AC_. This indicates that _the image of a point
formed by a plane mirror is the same distance back of the mirror as the
point itself is in front of it_. This principle may be used in locating
the image of point _B_ at _B´_. Locating the position of the _end
points_ of an image determines the position of the whole image as
_A´B´_.
[Illustration: FIG. 356.--The image _A´B´_ is as far back of the mirror
_M N_ as the object _A B_ is in front of the mirror.]
=366. How the Image is Seen.=--Suppose the eye to be placed at _E_. It
will receive light from _A_ by reflection as if it came from _A´_.
Similarly light starting from _B_ reaches the eye from the direction of
_B´_. There is nothing back of the mirror _in reality_ that affects our
sight, the light traveling only in the space in front of the mirror. Yet
the action of the reflected light is such that it produces the same
effect as if it came from behind the mirror. Images such as are seen in
plane mirrors are called _virtual_ to distinguish them from _real_
images, in which light actually comes to the eye from the various parts
of the visible image, as from the real image formed by a projecting
lantern upon a screen, or by an aperture as in the pin-hole camera.
Real images therefore are those that can be obtained upon a screen while
virtual images cannot.
=367. Multiple Reflection.=--If the light from an object is reflected by
two or more mirrors various effects may be produced, as may be
illustrated by the _kaleidoscope_. This consists of three plane mirrors
so arranged that a cross-section of the three forms an equilateral
triangle. The mirrors are placed in a tube across the end of which is a
compartment with a translucent cover containing pieces of colored glass.
On looking through the tube, the reflections from the several surfaces
produce beautiful hexagonal designs.
[Illustration: FIG. 357.--Perspective view of "Pepper's ghost."]
[Illustration: FIG. 358.--Diagram of the "Pepper Ghost" illusion.]
=368. Optical Illusions by a Plane Mirror.=--The _illusion_ called
_Pepper's Ghost_ is typical of many illusions produced by reflection. It
may be illustrated by taking a piece of plate glass, _M-N_, a tumbler of
water, _W_, and a lighted candle, _C_, placed in a box, _B_, having one
side open and arranged as shown in perspective in Fig. 357, and in
section in Fig. 358. If the effect is produced in a darkened room, the
observer at _E_ sees a virtual image of the lighted candle as if it were
in the glass of water, the water being seen by transmitted light
_through_ the plate glass, the latter forming a virtual image of the
candle by reflection. Some of the illusions produced by this means are:
(_a_) the figure suspended in mid air; (_b_) the bust of a person
without a trunk; (_c_) the stage ghost; (_d_) the disappearing bouquet.
[Illustration: FIG. 359.--Action of a concave mirror on parallel rays of
light.]
[Illustration: FIG. 360.--Real image formed by a concave mirror.]
=369. Concave Mirrors.=--Another useful piece of physical apparatus is
the concave spherical mirror. It is frequently made from plano-convex
lenses by silvering the convex surface of the lens, thus making a
concave reflecting surface from the inner surface of the silvered part;
they are also made by polishing the inner surfaces of metallic spherical
shells. The concave mirror is represented in section in Fig. 359 by the
curve _MN_; _C_ is the _center of curvature_ or the center of the
surface of which this mirror _MN_ is a part; the line _VC_ through the
center _V_ of the mirror is called the _principal axis_; while any other
line passing through _C_ is called a _secondary axis_. The point midway
between the vertex _V_ and center of curvature _C_ is called the
_principal focus_, _F_. It is the point through which parallel incident
rays pass after reflection. The angle _MCN_ which the curve of the
mirror subtends at the center is called the aperture of the mirror. We
learned in Art. 361, the angle of reflection of a ray of light is always
equal to the angle of incidence no matter what the nature of the
reflecting surface may be. If the reflecting surface is a regular
concave surface, like the inner surface of a sphere, the rays of light
coming from a point source may after reflection come to a focus, forming
a real image. The two extreme points of an object should be selected for
locating its image; Fig. 360 shows the construction. The real images
formed by concave mirrors are always inverted. The principal focus of a
concave mirror may be observed by holding the mirror in a beam of
sunlight entering a darkened room. The sun's rays after reflection
converge to form a small, round, intense spot of light, which is a real
image of the sun, located at the principal focus of the mirror. The
distance of the principal focus from the mirror is the least distance
that a real image can be formed in front of a concave mirror.
=370. Virtual Images by Concave Mirrors.=--When light comes from a small
point situated between a concave mirror and its principal focus, the
reflected rays are divergent and hence no real image of the object can
be found in front of the mirror. But if the rays are extended behind the
mirror they will meet in a point called the _virtual focus_. This is the
point from which they appear to come. Any image of an object situated
between the principal focus and a concave mirror is therefore a virtual
image, erect and larger than the object. (See Fig. 361.)
[Illustration: FIG. 361.--Virtual image formed by a concave mirror.]
=371. Construction of Real Images.=--There are five positions at which
an object may be situated in front of a concave mirror, namely: (1)
_beyond C_; (2) at _C_; (3) _between C and F_; (4) _at F_ and (5)
_between F_ and _V_. There are two ways by means of which the image
formed at each of these positions may be located, namely; (1)
_experimentally_, by allowing the rays of light from a luminous body to
focus on a screen and (2) _diagrammatically_. By the latter method the
two rays of light are considered the course of each of which may easily
be determined; first, the ray which strikes the mirror parallel to its
principal axis and which after reflection passes through the principal
focus; second, the ray which passing through the center of curvature
strikes the mirror at right angles and therefore after reflection must
pass directly back along its incident path. Where these two reflected
rays intersect is located the real image of the object. Whenever these
two rays of light do actually intersect, as in Fig. 360, a real image
(_ab_) is formed of the object _AB_.
The points _A_ and _a_, _B_ and _b_ and others similarly situated on an
axis extending through the center of curvature _C_ are called _conjugate
foci_, for they are so related that an object being at either one, its
image will be found at the other.
[Illustration: FIG. 362.--Action of a convex mirror upon parallel rays
of light.]
=372. The Convex Mirror.=--There are few practical uses to which convex
mirrors can be put. They are sometimes used to give the chauffeur of an
automobile a view of the road behind him. It is then attached to the
wind shield by a short rod. The reflected rays coming from a Convex
mirror are always divergent (see Fig. 362), hence the image is always
virtual and located behind the reflecting surface. The method of
construction for images formed by a convex mirror is similar to that for
concave mirrors. (See Fig. 363.) The center of curvature and principal
focus are behind the mirror and consequently the reflected rays have to
be produced backward until they meet. The images are always _virtual_,
_erect_ and _smaller_ than the object.
[Illustration: FIG. 363.--Construction of an image by a convex mirror.]
[Illustration: FIG 364.--Illustrations of Spherical Aberration.]
=373. Spherical Aberration.= Sometimes in a concave mirror when the
aperture _MCN_ (Fig. 364) is large the images are blurred or indistinct.
This is due to the fact that the incident rays near the outer edge of
the mirror do not focus after reflection at the same point as those
which pass into the mirror near the vertex, but cross the principal axis
at points between the mirror and principal focus as is shown in Fig.
364; this result is called _spherical aberration_. The larger the
aperture of the mirror the more the image is blurred. Concave mirrors in
practical use do not have an aperture much greater than 10 degrees. This
non-focusing of the rays of light by curved reflecting surfaces may be
noticed in many places, as when light is reflected from the inside of a
cup that contains milk or from the inside of a wide gold ring placed on
top of a piece of white paper. The pupil will note other instances.
This curve of light observed is called the _caustic by reflection_.
=374. Parabolic Mirrors.=--The best possible surface to give to concave
mirrors is parabolic. This is a curve which may be generated by moving a
point so that its distance from a fixed point and a fixed line are
always equal. If a source of light is placed at _F_ the rays after
reflection are rendered parallel. See Fig. 365. This reflector is used
in automobile lamps, headlights of locomotives, search-lights, etc. It
is also used in large reflecting astronomical telescopes to collect as
large an amount of light as possible from distant stars and bring it to
a focus. Such mirrors may be made exceedingly accurate.
[Illustration: FIG. 365.--Parabolic mirror.]
Important Topics
1. Reflection: regular, diffused; plane mirrors; laws of reflection.
2. Formation and location of images by plane mirrors. Wave and ray
diagrams.
3. Multiple reflection, illusions.
4. Curved mirrors, uses; concave, convex, parabolic.
Exercises
1. Distinguish between regular and diffused reflection. By means of
which do we see non-luminous bodies?
2. Could a perfect reflecting surface be seen? Explain.
3. A pencil is stood upright in front of a plane mirror set at an angle
of 45 degrees to the vertical. Shown by a diagram the location and
position of the image.
4. Show by diagrams the position and location of the images of a pencil
(a) when standing erect and in front of a _vertical_ mirror. (b) when
standing upon a horizontal mirror.
5. What is the difference between a real and a virtual image?
6. A standard candle and a lamp give equal illuminations to a screen
that is 1 ft. from the candle and 6 ft. from the lamp. What is the
candle power of the lamp? Explain.
7. Why are walls finished in rough plaster or painted with soft tones
without gloss better for schoolrooms than glossy paints or smooth white
plaster?
8. Try to read a printed page by looking at its image in a mirror. write
your name backward on a sheet of paper, and then look at the image of
the writing in a mirror. What effect is produced by the mirror in each
case?
9. If the point of a pencil is held to the surface of a piece of
plate-glass mirror two or more images may be seen in the mirror.
Explain.
10. Given a small lighted candle, a concave mirror, a meter stick, and a
white screen, how would you prove the statements made in Arts. 369 and
370 concerning the location of images formed by concave mirrors? Make
the diagram in each case.
11. Why do images seen in a quiet pond of water appear inverted? Explain
by a diagram.
(4) REFRACTION OF LIGHT
=375. Common Examples of Refraction.=--Everyone has noticed the apparent
bending of an oar, of a stick, or of a spoon when placed in water (see
Fig. 366), while many have observed that the bottom of a pond or stream
looks nearer to the surface than it really is. These and similar
illusions are due to the _refraction_ or bending of light rays as they
pass from one medium to another. The principles of refraction are among
the most useful found in the study of light since application is made of
them in the construction and use of important optical instruments, such
as the camera, microscope, telescope, and the eye.
[Illustration: FIG. 366.--The stick appears to be bent on account of
refraction.]
=376. Action of Light Undergoing Refraction.=--If a beam of sunlight be
admitted to a darkened room and reflected by a mirror so that it strikes
the surface of water in a glass jar, a part of the beam may be seen to
be reflected while another portion is transmitted through the water
(Fig. 367). The reflected beam follows the law of reflection while the
transmitted beam is seen to be _refracted_, or to have its courses
slightly changed in direction upon entering the water. If the mirror is
turned so that the angle at which the light strikes the water is
changed, the amount of refraction or change of course of the light is
varied. When the light strikes the water perpendicularly there is no
refraction. On the other hand, the greater the angle at which the light
strikes the water the greater the bending.
[Illustration: FIG. 367.--Part of the ray is reflected and part passes
into the water and is refracted.]
[Illustration: FIG. 368.--Illustrating the laws of refraction of light.]
=377. Laws of Refraction.= The action of light on entering, passing
through, and leaving a great variety of substances has been carefully
studied. A summary of the results of these observations is given in the
following _laws of refraction_: I. _When light enters a transparent
body, perpendicularly, it passes on without changing its direction._
II. _When light enters a denser transparent body obliquely, it is bent
toward the perpendicular; when light enters a less dense body obliquely,
it is bent away from the perpendicular._ (See Fig. 368.)
=378. The cause of refraction= may be illustrated by considering a line
of men moving across a field and occupying at equal time intervals the
successive positions 1, 2, 3, etc., indicated in Fig. 369. Suppose that
the upper and lower parts of the field have a smooth hard surface, while
at the center is a strip of newly ploughed ground. The line will move
more slowly over the ploughed field than over the hard field. This will
result in a retardation of the end of the line first striking the soft
ground with a resulting change of direction of the line, _toward_ the
perpendicular to the edge of the field (_on entering the place of more
difficult travel_), and _away_ from the perpendicular on moving into a
place where _increased speed results_.
[Illustration: FIG. 369.--Diagram illustrating the cause of refraction.]
=379. Index of Refraction.=--By studying the change of direction of the
marching men as shown in Fig. 369 it is evident _first_ that it is due
to a difference in speed in the two media. It is not easy to measure the
speed of light in a medium. However, the amount of refraction may be
determined easily and from this the _relative_ speed may be computed.
The _number that expresses the ratio of the speed of light in air to its
speed in another medium is called the index of refraction of that
medium_. The relative speeds of light, or the indices of refraction for
some substances, are: water, 1.33, crown glass, 1.51, flint glass,
1.61, diamond, 2.47, carbon bisulphide, 1.64.
[Illustration: FIG. 370.--The incident ray and the emergent rays are
parallel.]
=380. Plates, Prisms, Lenses.=--The refraction of light is usually
observed when it is passing through a plate, a prism, or a lens. The
important differences between the effects of each in refracting light
are illustrated in Figs. 370, 371 and 372. In Fig. 370 it is seen that
the refraction of the ray on entering the glass is counteracted by the
refraction away from the perpendicular upon leaving it. So that the
entering and emergent rays are _parallel_. In Fig. 371 the refraction at
the two surfaces of the prism results in a change of direction of the
ray, the course being bent toward the _thicker_ part of the _prism_. In
Fig. 372 it may be noticed that the convex lens resembles two prisms
with their bases together. Since all parts of the lens refract light
toward the thicker part, the center, the effect of the convex lens is to
bring the rays of light to a focus, at _F_.
[Illustration: FIG. 371.--Effect of a prism upon a ray of light.]
[Illustration: FIG. 372.--The convex lens brings the rays of light to a
focus.]
=381. Total Reflection.=--It has been shown that when light passes from
a _denser to a lighter_ medium, as from glass or water to air, that the
beam is refracted _away_ from the perpendicular. This is illustrated in
Fig. 373. The diagram represents the change in the course of a ray of
light that passes through water to a surface with air above it. A ray
striking perpendicularly passes through without refraction. Other rays
show increasing refraction with increasing angle of incidence. For one
ray the angle of refraction is so large that the refracted ray is
parallel to the surface. When this condition is reached, the _angle of
incidence_ is called the _critical angle_. Any increase in the angle of
incidence causes all of the light to be reflected as is the beam _E_.
This action is called _total reflection_, the course of the reflected
ray being according to the law of reflection. _A right-angle prism_ (see
Fig. 374) is often used where a mirror would ordinarily be employed, the
total reflection occurring within the prism giving more satisfactory
results than a mirror. See Art. 398 for a description of the Zeiss
binocular field-glass for an example of this use of total reflection.
[Illustration: FIG. 373.--An example of total reflection.]
[Illustration: FIG. 374.--Total reflection in a right-angle prism.]
The mirage (see Fig. 375) is an optical illusion by which distant
objects, below the horizon, are sometimes plainly seen. This
phenomenon is most frequently observed in hot, desert regions, when
the air conditions are such that the lower strata near the ground
are very much hotter than those above. These lower strata, having
expanded the most, are less dense than the cooler ones above. Hence
a ray of light traveling obliquely downward is refracted more and
more until total reflection takes place. The images seen are
inverted giving a representation of trees or other objects
reflected on the surface of still water. The mirage is also
frequently seen at sea, ships being observed, sometimes erect,
sometimes inverted, apparently sailing in the clouds near the
horizon. Over the Great Lakes, trees, boats, and towns on the
opposite shore, sixty or seventy miles away, can sometimes be
plainly seen, apparently but a few miles out. In this case the
images are erect, the total reflection being from warm, still
layers of air over colder layers near the water.
[Illustration: FIG. 375.--Diagram of a mirage.]
Important Topics
(A) Refraction: cause, illustration, two principles.
(B) Index of refraction, meaning.
(C) Plates, prisms, lenses, action of each.
(D) Total reflection, uses.
Exercises
1. Compute the speed of light in water, the index of refraction being
1.33.
2. If one wished to shoot a fish under water, should he aim at the
apparent location of the fish as viewed from the air? Explain, using a
diagram.
3. Define refraction. Mention two illustrations of this action that you
have observed out of school.
4. Why does the moon look larger near the horizon?
5. Is your reflection seen in a pool of water upside down? Why?
6. Why does it whiten molasses candy to pull it?
7. When looking at a building through the ordinary glass of a window why
do straight lines of the building appear to be so distorted? What makes
them appear to move as you move your head slightly?
8. Explain the phenomenon which one observes when looking at an object
through the air arising from a hot stove or radiator.
9. Frequently the horizontal diameter of the setting sun appears to be
greater than the vertical. Explain.
10. Explain why one observes several images of a luminous body like a
lighted candle when the reflected light from a thick glass mirror enters
the eye, the angle of reflection being large.
(5) THE FORMATION OF IMAGES BY LENSES
=382. Uses of Lenses in Optical Instruments.=--The use of instruments
that employ lenses in their operation, such as spectacles, reading and
opera glasses, and the camera, microscope, and telescope, is familiar to
most students of physics. The part played by the lenses, however, is not
generally understood. Consequently the study of the formation of images
by lenses is of general interest and importance.
=383. Forms of Lenses.=--While a lens may be formed from any transparent
solid it is commonly made of glass. It may have two curved surfaces or
one curved and one plane surface. Most lenses are _spherical lenses_,
since their curved surfaces form a part of the surface of a sphere. Fig.
376 represents a spherical lens with a curved surface coinciding with
that of a sphere whose center is at _C_. This center is called the
_center of curvature_, while the radius of the sphere _R_, is the
_radius of curvature_.
[Illustration: FIG. 376.--Formation of a spherical lens.]
There are two classes of lenses: those thick in the middle are called
_convex_, while those thick at the edges are _concave_. The mode of
constructing the six forms of spherical lenses is shown in Fig. 377.
These are named as follows: (1) double convex, (2) plano convex, (3)
concavo-convex, (4) double concave, (5) plano concave, (6)
convexo-concave.
[Illustration: FIG. 377.--Forms of Lenses. 1. double convex; 2. plano
convex; 3. concavo convex; 4. double concave; 5. plano concave; 6.
convexo concave.]
[Illustration: FIG. 378.--The action of a burning glass.]
=384. Effect of Lenses upon Light.=--The most important characteristic
of a lens is its effect upon a beam of light. Most persons have seen a
"burning glass," a double convex lens, used to bring to a point, or
focus, a beam of sunlight. To show the action of a burning glass send a
beam of light into a darkened room, and place in its path a double
convex lens. (See Fig. 378.) If two blackboard erasers are struck
together near the lens, the chalk particles in the path of the light are
strongly illuminated, showing that the light after passing through the
lens it brought to a focus and that it spreads out beyond this point.
This point to which the cone of light rays converges after passing
through the convex lens is called the _principal_ focus of the lens. The
distance from the principal focus to the center of the lens is the
_focal length_ or _principal focal distance_ of the lens. _The focal
length of double convex lenses of crown glass is about the same as the
radius of curvature of either surface._ The action of a convex or
converging lens upon light may be better understood by studying Fig. 379
in which light is passing from _S_ to _F_. The successive positions and
shape of the advancing light waves are indicated by lines drawn across
the beam. The light being retarded more in the thicker part of the lens,
the light waves on leaving the lens have a concave front. Since light
waves tend to move at right angles to the front of the wave, the light
is brought to a focus. After passing the focus the waves have a convex
front, forming a diverging cone.
[Illustration: FIG. 379.--Wave diagram of light passing through a convex
lens.]
=385. Concave Lenses.=--When sunlight passes through a _concave_ lens a
diverging cone of light is formed. (See Fig. 380.) This is caused by the
edges of the wave being retarded more than the center, producing a
convex wave front. This diverging cone of light acts as if it had
proceeded from a luminous point at _F_.
This point is called a _virtual_ focus and is nearly at the center of
the curvature of the nearer surface.
[Illustration: FIG. 380.--Wave diagram of light passing through a
concave lens.]
=386. The Formation of Images by Lenses.=--If a beam composed of
_parallel_ rays of light, as sunlight, is sent in turn through three
convex lenses of the same diameter but of different thickness, it is
found that the _thicker the lens the greater is its converging power, or
the shorter is its focal_ length. (See Fig. 381.) Now if a luminous
body, such as a lighted candle, be placed near the convex lens but
_beyond its focal length_, the light will be brought to a focus upon the
other side of the lens and an image of the candle may be clearly seen
upon the screen placed at this point. (See Fig. 382.) _The two points so
situated on opposite sides of a lens that an object at one will form an
image at the other are called conjugate foci._
[Illustration: FIG. 381.--The thicker the lens, the shorter is its focal
length.]
[Illustration: FIG. 382.--_C_ and _S_ are at conjugate foci.]
It will be helpful to compare the images formed of a candle by an
_aperture_ and by a _convex_ lens. Rays of light from each point of the
luminous body pass through the aperture in straight lines and produce
upon the screen a lighted space of the same shape as the candle. This
image is rather _hazy_ in outline. Each cone of rays from luminous
points of the flame is brought by the lens to a focus on the screen,
producing a _sharp image_. It is the converging power of convex lenses
that enables them to produce clear images.
[Illustration: FIG. 383.--Construction of a real image by a convex
lens.]
=387. The Construction of Diagrams to Represent the Formation of Images
by Lenses.=--Just as the earth has an axis at right angles to its
equator to which are referred positions and distances, so a lens has a
_principal axis_ at right angles to its greatest diameter and along this
axis are certain definite positions as shown in Fig. 383. Let _MN_ be
the _principal axis_ of a convex lens, _P_ and _P´_ are _principal foci_
on either side of the lens, _S_ and _S´_ are _secondary foci_. These are
at points on the principal axis that are twice as far from _O_, the
center of the lens, as are the principal foci. In the formation of
images by a convex lens, several distinct cases may be noticed:
(A) If a luminous body is at a _great distance_ at the left, its light
is brought to a _focus_ at _P_, or its _image is formed at P_. (B) As
the _object approaches_ the lens the _image gradually recedes_ until the
object and image are at _S_ and _S´_, _equally distant from O and of
equal size_ (as in Fig. 383). The object and image are now said to be at
the _secondary foci_ of the lens. (C) As the _object moves from S to P_
the image recedes, rapidly increasing in size until (D) when the object
is at _P_ the rays become parallel and no image is formed. (E) When the
object is between _P_ and the lens, the rays _appear to proceed from
points back of the object_, thus forming an _erect, larger, virtual
image_ of the object. (See Fig. 384.) This last arrangement illustrates
the _simple microscope_.
With a concave lens but one case is possible, that corresponding to the
one last mentioned with convex lenses; since the rays from a body are
divergent after passing through a concave lens they appear to proceed
from points _nearer_ the lens than the object and hence a _virtual,
erect, smaller image_ of the object is formed. This virtual image may be
seen by looking _through_ the lens toward the object. (See Fig. 385.)
[Illustration: FIG. 384.--Construction of a virtual image by a convex
lens.]
[Illustration: FIG. 385.--Construction of a virtual image by a concave
lens.]
=388. The Lens Equation.=--The location of either the object or of the
image upon the principal axis of the lens may be calculated if the
position of one of these and the focal length are known. This is
accomplished by the use of a formula 1/_F_ = 1/_D_{0}_ + 1/_D_{1}_ in
which _F_ represents the focal length and _D_{0}_ and _D_{1}_ the
distance from the lens of the object and the image respectively. Thus if
an object is placed 30 cm. from a lens of 10 cm. focal length, where
will the image be formed? Thus: 1/10 = 1/30 + 1/_D_ and 3_D_{1}_ =
_D_{1}_ + 30, or 2_D_{1}_ = 30 _D_{1}_ = 15. This result indicates that
a real image will be 15 cm. from the lens. A minus value would indicate
a virtual image.
Important Topics
(A) Lenses: convex, concave, six forms, center and radius of curvature.
(B) Principal focus, focal length, virtual focus, conjugate foci.
(C) Principal axis, images formed when object is in various locations.
(D) Computation of location of images.
Exercises
1. Why is an image of a candle formed by an aperture, not sharply
defined?
2. When a photographer takes your picture and moves the camera nearer
you, must he move the ground glass screen toward the lens or away
from it? Explain.
3. How can you find the principal focal length of a lens.
4. How can you test a spectacle lens to see whether it is convex
concave?
5. When will a convex lens produce a virtual image? Have you ever seen
one? Where?
6. When a photographer wishes to obtain a full length view of a person,
where does he place the camera?
7. The focal length of the lens is 24 cm. How far from the lens must an
object be placed in order that a real image may be three times as long
as the object?
8. There is a perfect image of an object on the ground glass of a
camera. The center of the lens is 20 cm. in front of the image and the
object 75 cm. from the lens. What is the focal length of the lens?
9. An object is 60 cm. from the lens, the image 120 cm. from it. Find
the focal length.
10. How can you find experimentally the principal focal length of a
lens?
11. A lens is used to project an enlarged image of a candle upon a
screen. Which is farther from the lens, the candle or the image?
Explain.
(6) OPTICAL INSTRUMENTS
=389. The Eye.=--The most common optical instrument is the _eye_. While
the structure of the eye is complicated, the principle of it is simple,
involving the formation of an image by a double convex lens. (See Fig.
386, in which is shown a front to back, vertical cross-section of the
eye.) The eye appears to be made of portions of two spheres, one of
which, smaller than the other, is placed in front. This projecting part
is transparent, but refracts the light which strikes it obliquely, so as
to turn it into the eye. This enables us to see objects at the side when
looking straight ahead. Test this by looking directly in front of you
and see how far back on each side of the head you can notice a movement
of the forefinger of each hand.
[Illustration: FIG. 386.--Cross-section of the eye.]
=390. Action of the Eye in Vision.=--When we look at an object, a small,
real, inverted image is formed upon the _retina_ at the back of the
interior of the eye. The retina is an expansion of the optic nerve and
covers the inner surface at the back of the eyeball. Seeing is due to
the action of light in forming images upon the retina. Our eyes are so
constructed that when they are relaxed the lens is adjusted to form
clear images of _distant_ objects upon the retina. If we look from
distant to near objects without changing the shape of the eye lens, a
sharp image of the latter cannot be formed and we get a blurred
impression. It is difficult, however, to look at objects without
automatically adjusting the eye lens so that it will make a sharp image.
Test this by looking out of a window at a distant object, then without
moving the head or eyes look at the glass of the window; you will notice
a slight change of some sort _in_ the eye itself as the vision is
adjusted. This adjustment is made by muscles that pull or compress the
eye lens so as to make it thicker for near objects and thinner for
distant ones. The eye ordinarily does not see objects nearer than 10 in.
clearly. This means that the greatest possible thickening of lens will
not form clear images upon the retina if the object is nearer than 10
in. (25 cm.).
[Illustration: FIG. 387.--The visual angle, _AOB_ is greater at _AB_
than at _A´B´_.]
=391. The Visual Angle.=--To examine objects carefully we usually bring
them as close to the eye as possible, for the nearer to the eye the
object is brought, the larger is the visual angle formed by it (see Fig.
387), and the larger is its image upon the retina. _The visual angle of
an object is the angle at the eye lens between the rays that have come
from the ends of the object._ Consequently the more distant the object,
the smaller is its visual angle. Now if we wish to examine small objects
with great care, we frequently find that it is necessary to bring them
close to the eye so that they have a visual angle of adequate size. If
they must be brought closer than 10 in. a double convex lens is placed
in front of the eye. This assists the eye lens in converging the light
so that a clear image may be formed when the object is close, say an
inch or so from the eye. This is the principle of the magnifying glass
used by watch-makers and of the _simple microscope_. The action of the
latter is illustrated by Fig. 388. The convex lens forms a virtual,
enlarged image "_A´-B´_" of the object "_A-B_" which it observed instead
of the object itself.
[Illustration: FIG. 388.--Action of the simple microscope.]
[Illustration: FIG. 389.--"Near sightedness", or myopia. Parallel rays
come to a focus at _F_; emerging rays focus at _A_, the far point.]
=392. Defects of Vision.=--There are several defects of vision that may
be corrected by spectacles or eye-glasses. One of these is
"near-sightedness." It is due either to an eyeball that is elongated, or
to an eye lens that is too convex, or to both conditions. This condition
brings light from distant objects to a focus too soon (as shown in Fig.
389). Only light from near objects will focus upon the retina in such
cases. With _normal_ vision light from _distant_ or _near_ objects may
be focused without unusual effort upon the retina, see Fig. 390. The
remedy for near-sightedness is to use concave lenses which will assist
in properly refracting the light so the focus will be formed on the
retina (Fig. 391). "Far-sightedness" is the reverse of near-sightedness;
the eyeball is either too short, or the lens too flat, or both
conditions obtain, so that the light entering the eye is brought to a
focus behind the eyeball (Fig. 392). The remedy is convex lenses which
will assist in properly converging the light, see Fig. 393. A third
defect is called _astigmatism_. This is caused by some irregularity or
lack of symmetry in the eye. It is corrected by a _cylindrical_ lens
that compensates for this defect of the eye. A diagram similar to Fig.
394 is used as a test for astigmatism. If the lines appear with unequal
distinctness, some irregularity of refraction (astigmatism) is
indicated.
[Illustration: FIG. 390.--The normal eye. The parallel rays _A B_ focus
without accommodative effort at _C_.]
[Illustration: FIG. 391.--Correction of near-sightedness by concave
lens.]
[Illustration: FIG. 392.--Far-sightedness or hyperopia. Parallel rays
focused behind the retina.]
[Illustration: FIG. 393.--Correction of far-sightedness by a convex
lens.]
[Illustration: FIG. 394.--Test card for astigmatism.]
=393. The Photographic Camera.=--This is a light-tight box, provided
with a convex lens in front, covering an aperture and a ground glass
screen at the back. The distance between the lens and the screen is
adjusted until a sharp image is obtained upon the latter, which is then
replaced by a sensitive plate or film. The sensitized surface of the
plate or film contains a salt of silver which is changed by the action
of light. After the plate has been "exposed" to the action of light, it
is "developed" by the use of chemicals producing a _negative_ image.
From "negative," by the use of sensitized paper, "positive" prints may
be secured which resemble the object photographed.
[Illustration: FIG. 395.--Diagram of the projecting lantern.]
=394. The projecting lantern= (see Fig. 395) employs a strong source of
light, as an electric arc lamp _L_, to strongly illuminate a transparent
picture, or _lantern slide_, _S_, a real image (_I_) of which is formed
upon a large screen. Two large plano-convex lenses (_C_), called
condensing lenses, are placed near the lamp to concentrate the light
upon the "slide" _S_. The convex lens forming the image is called the
"objective" (_O_).
=395. The compound microscope= consists of two lenses. One called the
_objective_ is placed near the object to be viewed. This lens has a
short focal length usually less than a centimeter. It forms a _real
image_ of the object. _A´_-_B´_. The other lens, the _eyepiece_ forms a
virtual image of this real image. _A´´_-_B´´_. (See Fig. 396.)
=396. The telescope= consists of two lenses, the eyepiece and the
objective. As in the compound microscope, the objective of the telescope
forms a real image of the distant object, the eyepiece forming an
enlarged virtual image of the real image. It is the virtual image that
is viewed by the observer. (See Fig. 397.) In order to collect
sufficient light from distant stars the objective is made large,
sometimes 50 in. in diameter.
[Illustration: FIG. 396.--Formation of an image by a microscope. _A_-_B_
is the object. _B´_-_A´_ the real image formed by the "objective."
_B´´_-_A´´_ is the virtual image formed by the eyepiece. The eye sees
the virtual image.]
The length of the telescope tube depends upon the focal length of the
objective, since the distance between the two lenses must equal the
_sum_ of their focal lengths.
[Illustration: FIG. 397.--Formation of an image by a telescope. _b_-_a_
is the real image; _d_-_c_ is the virtual image seen by the observer.]
=397. The opera glass= consists of a convex lens as objective and a
_concave_ lens as an eyepiece. The former tends to form a real image but
the latter diverges the rays before a real image can be formed, the
action of the two lenses producing an enlarged virtual image (as in Fig.
398) which is viewed by the one using the glass. The compact size of
the opera glass is due to the fact that the distance between the two
lenses is the _difference_ of the focal lengths.
[Illustration: FIG. 398.--Formation of an image by an opera-glass.
_a_-_b_ is the virtual image.]
[Illustration: FIG. 399.--Diagram of the Zeiss binocular or prism field
glass.]
=398. The Prism Field Glass or Binocular.=--This instrument. has come
into use in recent years. It possesses the wide field of view of the spy
glass but is as compact as the opera glass. This compact form is secured
by causing the light to pass back and forth between two right-angle
prisms (as shown in Fig. 399). This device permits the use of an
objective lens with a focal length three times that of the tube,
securing much greater magnifying power than the short instrument would
otherwise possess. A further advantage is secured by the total
reflection from the two prisms, one of which is placed so as to reverse
the image right for left and the other inverts it, so that when viewed
in the eyepiece it is in its proper position.
Important Topics
1. The eye: parts, formation of image, kind, how, where.
2. Eye defects, how remedied. Visual angle.
3. Simple microscope, camera; images, kind, how formed.
4. Compound microscope, telescope and opera glass; images, action of
each lens.
Exercises
1. Name three instruments in which lenses form virtual images and three
in which _real_ images are formed.
2. In what direction is an oar in water apparently bent? Explain by a
diagram.
3. What optical instruments have you used? Is the _visible_ image formed
by each of these _real_ or _virtual_?
4. The focal length of a copying camera lens is 14 in. Where must a
drawing be placed so that an image of the same size may be formed upon
the ground glass screen? What must be the distance of the screen from
the lens?
5. What are two methods by which you can determine the focal lengths of
the lens of a photographic camera?
6. The critical angle for water is 48-1/2 degrees. Show by a diagram how
much of the sky can be seen by a diver who looks upward through the
water.
7. How is near-sightedness caused? How is it corrected? Illustrate by a
diagram.
8. How is the eye accommodated (focused) as an object gradually
approaches it?
9. Explain why a simple microscope assists in looking at the parts of a
flower or insect.
10. Why do people who have good eyesight when young require glasses as
they grow old?
(7) COLOR AND SPECTRA
[Illustration: GUGLIELMO MARCONI
"Copyright by Underwood & Underwood, N. Y."
Guglielmo Marconi (Italy). Inventor of wireless telegraphy.]
[Illustration: ALEXANDER GRAHAM BELL
"Copyright by Underwood & Underwood, N. Y."
Alexander Graham Bell, Washington, D. C. Inventor of the telephone.]
=399. Color.=--Much of the pleasure experienced in gazing at beautiful
objects is due to the _color_ shown by them. The blue sky, the green
grass, and the varied tints of flowers, and of the rainbow all excite
our admiration The study of color begins naturally with the production
of the _spectrum_, the many-colored image upon a screen produced by
passing a beam of light through a prism. The spectrum is best shown when
the light enters by a narrow slit (Fig. 400). The spectrum was first
produced by Sir Isaac Newton in 1675 by the means just described. The
names usually given to the more prominent colors of the spectrum are
violet, indigo, blue, green, yellow, orange, and red. The initials of
these names, combined, spell _vibgyor_, a word without meaning except to
assist in remembering the order of the colors in a spectrum. If the
light that has passed through a prism is sent through a second prism
placed in reverse position (see Fig. 401), the light passing through
both prisms is found to be white. This experiment _indicates that white
light is composed of light of all colors_.
[Illustration: FIG. 400.--Formation of the spectrum by a prism.]
[Illustration: FIG. 401.--The colors of the spectrum recombine to form
white light.]
=400. Dispersion.=--The separation of the colors by a prism is called
dispersion. In experimenting to find a reason for dispersion, it has
been learned that lights of different colors are of different wave
lengths. Color in light is therefore analogous to pitch in sound. We
hear through many octaves, but we see through about one octave. That is,
the shortest visible waves of violet light are about 0.000038 cm. in
length while the longest visible red rays are 0.000076 cm., or the
longest visible light waves are about twice the length of the shortest
visible ones. It appears from the evidence of experiments upon
dispersion that _light waves of different lengths are refracted
differently_. This causes the images formed by refraction through simple
glass lenses to be fringed with color and to lose some of their
sharpness and definiteness of outline, since the violet light is brought
to a focus sooner than the red. (See Fig. 402.) This seriously affects
the value of such lenses for optical purposes. Fortunately it is found
that _different kinds of glass have a different rate of dispersion for
the same amount of refraction_.
[Illustration: FIG. 402.--Violet light comes to a focus sooner than
red.]
=401. The Achromatic Lens.=--The existence of these different kinds of
glass makes possible a combination of lenses in which dispersion is
entirely overcome with the loss of only about one-half of the
refraction. Such a combination is shown in Fig. 403. It is called an
_achromatic lens_, since images formed by it are not colored but white
(_a_ = without, _chroma_ = color). _The achromatic lens consists of a
double convex lens of crown glass combined with a plano-concave lens of
flint glass._ Achromatic lenses are used in all high-grade optical
instruments such as telescopes and microscopes. The colored images that
are sometimes seen in cheap opera glasses show the result of not using
achromatic lenses.
[Illustration: FIG. 403.--An achromatic lens. _C_ is of crown glass;
_F_, of flint glass.]
=402. The Color of Bodies.=--Project the spectrum of sunlight upon a
white surface in a darkened room.
Now place in different parts of the spectrum objects of various
colors. Red objects will show brilliant red when at the red end of
the spectrum but look black at the blue end, while blue objects
appear blue only at the blue end.
These facts indicate that the color of an object depends upon two
things: (a) _the light that falls upon it and_ (b) _the light which it
sends to the eye_. A _black_ surface absorbs all color while a _white_
one reflects all wave lengths to the eye in the same proportion that
they come to it. A white object will appear red in red light, and blue
in blue light since it reflects both of these. A _colored_ object
reflects light of its own color but absorbs all others. The color then
of a body is due to the light which it does not absorb, but which comes
from it to the eye.
_403. The color of transparent bodies_, such as colored glass, is due to
the presence of a _dye_ or _pigment_ contained in the body. This pigment
absorbs a part of the light, the part transmitted giving the color. This
may be shown by holding a sheet of colored glass in a beam of light
either before or after it has passed through a prism. Some colors, as
red, may be found to be nearly _pure_, only the red passing through,
while green glass often transmits in addition to the green some yellow
and some red light.
=404. Complementary Colors.=--If two prisms are placed in reversed
position near each other (see Fig. 401), a beam of light dispersed by
one is recombined into white light by the other. If now a card is held
between the two prisms so as to cut off some of the colored light, say
the red, the remaining light will be found to form a _greenish blue_. If
the card is removed, the light becomes _white_ again. That is, red and
_peacock blue_ light together form white. Any two colors that together
form white light are called _complementary_. Other complementary colors
are light yellow and blue, green and crimson, orange and greenish blue,
violet and greenish yellow. We must not confuse the combining of colors
(light) and the combining of _pigments_, the latter consisting of bodies
that absorb light. Yellow pigment absorbs all but yellow and some green,
while blue pigment absorbs all but blue and some green. Mixing these two
pigments causes the absorption of all colors but _green_. Blue and
yellow _paint_ mixed produce _green_, while blue and yellow _light_ give
white.
=405. The solar spectrum=, as the spectrum of sunlight is called, may be
observed in the _rainbow_. The latter is produced through the dispersion
of light by spherical raindrops. Its formation may be imitated by
sending a small circular beam of light through a screen against a round
glass flask filled with water. (See Fig. 404.) The light passes through
the water and is dispersed when it enters and when it leaves, producing
a color upon the screen at _R_-_V_. The course of the light within the
drop is indicated in Fig. 405. The violet ray comes to the eye more
nearly horizontal and is therefore below red, as we look at the rainbow.
=406. Fraunhofer Lines.=--Some of the most important features of the
solar spectrum are not seen in the rainbow or in the band of light
usually observed upon a screen. By the use of a narrow slit and a
convex lens to carefully focus the slit upon a white screen it is seen
that the solar spectrum is crossed by many _dark_ lines. These are
called Fraunhofer lines, to honor the German scientist who in 1814 first
accurately determined _their_ position. Two experiments _with a
spectroscope_ will help to make clear the meaning of the Fraunhofer
lines.
[Illustration: FIG. 404.--A rainbow formed by a beam of light striking a
flask of water.]
[Illustration: FIG. 405.--The course of a beam of light within a drop of
water.]
=407. The Spectroscope and Its Uses.=--The spectroscope (Fig. 406) is an
instrument for observing spectra. It consists of a prism, a slit, and a
convex lens _T_ for focusing an image of the slit accurately upon a
screen (Fig. 407) where the spectrum is observed through the eyepiece
_E_.
[Illustration: FIG. 406.--The spectroscope.]
(A) A Bunsen flame is placed in front of the slit and a heated platinum
wire which has been dipped in common salt or some sodium compound placed
in the Bunsen flame; the latter becomes yellow and a vivid yellow line
is observed on the screen in the spectroscope. Other substances, as
barium and strontium salts, when heated to incandescence in the Bunsen
flame, give characteristic bright lines. In fact each _element_ has been
found to have its own characteristic set of colored lines. This fact is
made use of in _spectrum analysis_, by which the presence of certain
elements in a substance can be definitely proved upon the appearance of
its particular lines in the spectrum.
[Illustration: FIG. 407.--Diagram of a spectroscope.]
[Illustration: FIG. 408.--The bright line spectrum of iron and its
coincidences with some of the dark lines of the solar spectrum.]
(B) If light from, for example, an arc light is sent over a gas flame
containing _sodium_ vapor, a _dark line_ appears in the spectrum--in
the exact position in which the yellow sodium line appeared. It seems
that the sodium vapor removes from white light the same wave lengths
that it itself produces. This absorption is supposed to be due to
sympathetic vibration; just as a tuning fork is set in vibration by the
waves of another fork in unison with it, at the same time absorbing the
wave energy, so in the gas flame the sodium particles absorb the wave
motion of the same vibration rate as that emitted by them. The fact that
the spectrum of sunlight contains a great many dark lines is believed to
indicate that the sun is surrounded by clouds formed by the vaporization
of the various substances in the sun itself. By comparing the dark lines
of the solar spectrum with the _bright-line spectra_ of various
substances found in the earth, such an exact correspondence of the lines
is found that the presence of the vapor of these substances about the
sun is considered proved. (See Fig. 408 which shows the exact
correspondence between the bright-line spectrum of iron vapor and the
dark lines appearing in a portion of the sun's spectrum.) The spectra of
the stars also contain certain dark lines. Thus the presence of the
corresponding substances in distant stars is considered as determined.
=408. Theory of Color Vision.=--By combining light of the _three colors_
_red_, _green_ and _blue-violet_ in proper proportions, it has been
found possible to produce any color effect, even white. This leads to
the conclusion that in the retina of the eye are three different kinds
or sets of sensitive nerve endings, sensitive respectively to red, to
green, and to blue light. This idea is given corroboration by some facts
of color blindness. Thus some persons have no sensation of _red_, this
color not being distinguished from green. Others are color blind to
green or blue. It is supposed that in color blind persons one of the
sets of nerve endings sensitive to one of these three colors is lacking.
=409. Three-color Printing.=--Since all colors may be produced by mixing
the three colors, light red, green, and blue-violet, these are called
_the three primary colors_. The so-called primary pigments or paints are
simply the complements of the three primary colors. They are, in order,
peacock blue, crimson, and light yellow. The three pigments when mixed
yield black, since combined they absorb all kinds of visible light. The
process of three-color printing, now so generally employed in printing
colored pictures for books, calendars, etc., consists in combining upon
white paper three colored impressions, using successively the three
primary pigments (yellow, crimson and blue) from plates prepared as
follows:
Three photographs of a given colored object are taken, each through a
different sheet of gelatine called a filter, stained the color of one of
the primary colors. From these photographs half-tone blocks are made in
the usual way. The colored picture is made by carefully superposing
impressions from these blocks, using in each case an ink whose color is
the complement of the "filter" through which the original picture was
taken. An illustration of the process is given upon the plate in the
frontispiece of this book.
Important Topics
1. Color, due to wave length; dispersion by prism, sphere in rainbow,
complementary colors, color of opaque and transparent bodies.
2. Spectra, solar; formation of rainbow; bright-line spectra, how
formed, how used; dark-line, how formed, used.
3. Theory of color vision. Three color printing.
Exercises
1. How does a white flower look when viewed through a blue glass?
Through a red glass? Through a red and blue glass at the same time?
2. Why does a red ribbon appear black when seen by blue light and red
when seen by red light?
3. In what part of the sky must you look to see a rainbow in the
morning? In the afternoon? Explain.
4. How would you arrange two similar prisms so as to produce double the
deviation produced by one?
5. The color of an object depends upon what two things?
6. What kind of a spectrum should moonlight give? Why?
7. A mixture of green and red lights gives a sensation of yellow. Can
you suggest why a mixture of blue and yellow lights gives the sensation
of white?
(8) NATURE OF LIGHT, INTERFERENCE, POLARIZATION
=410. The Corpuscular Theory.=--The theory of the nature of light that
was most generally accepted until about the year 1800, held that light
consists of streams of minute particles, called corpuscles, moving at
enormous velocities. This _corpuscular theory_ was in accord with the
facts of reflection and the _rectilinear_ motion of light, but was
abandoned after the discovery of the _interference of light_, as it
could not account for the latter phenomenon.
=411. The Wave Theory of Light.=--The theory that _light is_ a _form of
wave motion_ was first advanced by Huygens, a Dutch physicist, in the
seventeenth century. This theory was opposed at the start since (A) _no
medium_ was known to exist which would convey wave motion through space,
as from the sun to the earth, and (B) the _rectilinear motion_ of light
was _unlike_ that of any _other_ form of known wave motions, such as
that of water or of sound waves which are able to bend around corners.
In answer to the first objection, Huygens assumed the presence of a
medium which he named _ether_, while the second objection has been
completely overcome during the past century by the discovery that _light
may deviate from a straight line_. It is now known that the _excessive
shortness_ of light waves is the reason for its straight-line motion.
Further, long ether waves, as those of wireless telegraphy, are found to
bend around obstacles in a manner similar to those of water or sound.
[Illustration: FIG. 409.--Two plates pressed together by a screw clamp.]
[Illustration: FIG. 410.--Illustrating the interference of light by a
thin film of air.]
=412. The interference of light= is one of the phenomena for which the
wave theory offers the only satisfactory explanation. Interference of
light may be shown by taking two pieces of plate glass and forcibly
pressing them together by a screw clamp, as shown in Fig. 409. After a
certain pressure has been reached, colored rings will appear about the
compressed spot when viewed by light _reflected_ from the upper surface
of the glass. If light of one color, such as that transmitted by red
glass, falls upon the apparatus, the rings are seen to be alternately
red and dark bands. The explanation of this phenomenon according to the
wave theory is as follows: The two sheets of glass, although tightly
pressed together, are separated in most places by a thin wedge of air
(see Fig. 410), which represents in an exaggerated form the bending of
the plates when pressed by the clamp. Several waves are represented as
coming from the right and entering the glass. Now the wave moving from
_R_ to the plates has some of its light reflected from each glass
surface. Consider the two portions of the wave reflected at each of the
surfaces between the plates, _i.e._, from the two surfaces of the wedge
of air. If the portion of the wave reflected from the second surface of
the air wedge combines with that reflected from the first surface, in
the _same phase_ as at _C_, the two reflected waves strengthen each
other. While if the two reflected portions of the wave meet in opposite
phases as at _A_ and _B_, a decrease or a complete extinction of the
light results. This is called _interference_. If light of one wave
length is used, as red light, the regions of reinforcement and
interference are shown by red and dark rings, while if white light is
used, the ring where red light interferes, yields its complementary
color, greenish blue. Where interference of greenish blue occurs, red is
found, etc. Many phenomena are due to interference, such as (A) the
color of thin films of oil on water, where the portions of light
reflected from the two surfaces of the oil film interfere resulting in
the production of color; (B) the color of soap bubbles. When first
formed, soap-bubble films are not thin enough to show interference well,
but as the bubbles increase in size or become thinner on standing, the
conditions for interference are reached and, as the film becomes
thinner, a regular succession of colors is noticed.
=413. Differences Between Light and Sound.=--Among the important
differences between light and sound that have been considered are the
following: the former are (a) _waves_ in the ether, (b) _of very short
wave length_, and (c) their _motion is in straight lines_. Another
difference (d) is in _the mode of vibration_.
Sound waves are _longitudinal, while light waves are transverse_. Light
waves consist of vibrations of the ether at right angles to the line of
motion. To illustrate the reasoning that has led to this conclusion,
suppose a rope to be passed through two vertical gratings. (See Fig.
411, 1.) If the rope be set in _transverse_ vibration by a hand, the
waves produced will readily pass through to the gratings _P_ and _Q_ and
continue in the part extending beyond _Q_. If, however, _Q_ is at right
angles to _P_, no motion will be found beyond _Q_. Now if a stretched
coiled spring with longitudinal vibrations should take the place of the
rope, it is evident that the crossed position of the two gratings would
offer no obstacles to the movement of the vibration. In other words,
crossed gratings offer no obstruction to longitudinal vibrations, while
they may completely stop transverse vibrations.
[Illustration: FIG. 411.--Transverse waves will pass through both
gratings in (1) where the openings in the two gratings are at right
angles. The waves passing _P_ are stopped by _Q_ (2).]
[Illustration: FIG. 412.--Effect of tourmaline crystals on light.]
=414. Polarization of Light.=--It is found that two crystals of
tourmaline behave toward light just as the two gratings behave with
respect to the transverse waves of the rope. Thus, if a small opening in
a screen is covered with a _tourmaline_ crystal, light comes through but
slightly diminished in intensity. If a second crystal is placed over the
first one so that the two axes are in the same direction as in Fig.
412_P_, light is as freely transmitted through the second crystal as
through the first, but if the crystals are crossed (Fig. 412_S_) no
light passes the second crystal. This experiment shows that the light
which has passed through one tourmaline crystal will pass through
another only when the latter is held in a certain position, hence it is
believed that a tourmaline crystal is capable of transmitting light
that is vibrating in one particular plane. The direct conclusion from
this is that _light waves_ are _transverse rather than longitudinal_.
The experiment just described illustrates what is called _polarization
of light_. The beam that after passing through _a_ (Fig. 412) is unable
to pass through _b_, if the two axes are crossed, is called a _polarized
beam_. The conclusion that light waves are transverse is therefore based
upon the phenomenon of the polarization of light. This was first
discovered by Huygens in 1690.
Important Topics
1. Interference of light: evidence, reasoning involved, illustration.
2. Polarization of light: evidence, reasoning involved.
3. Nature of light, differences between sound and light.
Exercises
1. Make a list of the differences between sound and light and state
briefly the evidence upon which the knowledge of these differences is
based.
2. Why will a thickness of film that will produce interference of red
light be different from that producing interference for green or blue?
3. Using the formula _n_ = _v_/_l_ compute the vibration rate for violet
light if its wave length is considered as 0.00004 cm.
4. Explain how the fact of polarization affects the wave theory of
light.
5. Show how it is possible by comparing the spectrum of the sun with
that of a star to tell whether the star is approaching or receding from
the earth.
Review Outline: Light
Light; speed, source, medium.
Straight Line Motion; shadow, umbra, penumbra, eclipse, image.
Photometry; Law of intensity, candle power, foot-candle.
Mirrors; Law of reflection; image--real, virtual; plane, curved,
parabolic, mirrors.
Refraction; cause and effects; plate, prism, lens; total reflection.
Lenses; six forms, principal focus, center, lens equation, 1/_F_ =
1/_D_{o}_ + 1/_D_{i}_.
Optical instruments; eye, defects and correction, camera, microscope,
etc.
Spectra; 3 kinds, dispersion, production of color effects, spectroscope,
uses.
Nature of Light; wave theory, interference, polarization, significance.