REFRACTION
107. Bent Rays of Light. A straw in a glass of lemonade seems to be
broken at the surface of the liquid, the handle of a teaspoon in a cup
of water appears broken, and objects seen through a glass of water may
seem distorted and changed in size. When light passes from air into
water, or from any transparent substance into another of different
density, its direction is changed, and it emerges along an entirely
new path (Fig. 64). We know that light rays pass through glass,
because we can see through the window panes and through our
spectacles; we know that light rays pass through water, because we can
see through a glass of clear water; on the other hand, light rays
cannot pass through wood, leather, metal, etc.
[Illustration: FIG. 64.--A straw or stick in water seems broken.]
Whenever light meets a transparent substance obliquely, some of it is
reflected, undergoing a change in its direction; and some of it passes
onward through the medium, but the latter portion passes onward along
a new path. The ray _RO_ (Fig. 65) passes obliquely through the air to
the surface of the water, but, on entering the water, it is bent or
refracted and takes the new path _OS_. The angle _AOR_ is called the
angle of incidence. The angle _POS_ is called the angle of refraction.
[Illustration: FIG. 65.--When the ray _RO_ enters the water, its path
changes to _OS_.]
The angle of refraction is the angle formed by the refracted ray and
the perpendicular to the surface at the point where the light strikes
it.
When light passes from air into water or glass, the refracted ray is
bent toward the perpendicular, so that the angle of refraction is
smaller than the angle of incidence. When a ray of light passes from
water or glass into air, the refracted ray is bent away from the
perpendicular so that the angle of refraction is greater than the
angle of incidence.
The bending or deviation of light in its passage from one substance to
another is called refraction.
108. How Refraction Deceives us. Refraction is the source of many
illusions; bent rays of light make objects appear where they really
are not. A fish at _A_ (Fig. 66) seems to be at _B_. The end of the
stick in Figure 64 seems to be nearer the surface of the water than it
really is.
[Illustration: FIG. 66.--A fish at _A_ seems to be at _B_.]
The light from the sun, moon, and stars can reach us only by passing
through the atmosphere, but in Section 76, we learned that the
atmosphere varies in density from level to level; hence all the light
which travels through the atmosphere is constantly deviated from its
original path, and before the light reaches the eye it has undergone
many changes in direction. Now we learned in Section 102, that the
direction of the rays of light as they enter the eye determines the
direction in which an object is seen; hence the sun, moon, and stars
seem to be along the lines which enter the eye, although in reality
they are not.
109. Uses of Refraction. If it were not for refraction, or the
deviation of light in its passage from medium to medium, the wonders
and beauties of the magic lantern and the camera would be unknown to
us; sun, moon, and stars could not be made to yield up their distant
secrets to us in photographs; the comfort and help of spectacles would
be lacking, spectacles which have helped unfold to many the rare
beauties of nature, such as a clear view of clouds and sunset, of
humming bee and flying bird. Books with their wealth of entertainment
and information would be sealed to a large part of mankind, if glasses
did not assist weak eyes.
By refraction the magnifying glass reveals objects hidden because of
their minuteness, and enlarges for our careful contemplation objects
otherwise barely visible. The watchmaker, unassisted by the magnifying
glass, could not detect the tiny grains of dust or sand which clog the
delicate wheels of our watches. The merchant, with his lens, examines
the separate threads of woolen and silk fabrics to determine the
strength and value of the material. The physician, with his invaluable
microscope, counts the number of infinitesimal corpuscles in the blood
and bases his prescription on that count; he examines the sputum of a
patient to determine whether tuberculosis wastes the system. The
bacteriologist with the same instrument scrutinizes the drinking water
and learns whether the dangerous typhoid germs are present. The
future of medicine will depend somewhat upon the additional secrets
which man is able to force from nature through the use of powerful
lenses, because as lenses have, in the past, been the means of
revealing disease germs, so in the future more powerful lenses may
serve to bring to light germs yet unknown. How refraction accomplishes
these results will be explained in the following Sections.
110. The Window Pane. We have seen that light is bent when it passes
from one medium to another of different density, and that objects
viewed by refracted light do not appear in their proper positions.
When a ray of light passes through a piece of plane glass, such as a
window pane (Fig. 67), it is refracted at the point _B_ toward the
perpendicular, and continues its course through the glass in the new
direction _BC_. On emerging from the glass, the light is refracted
away from the perpendicular and takes the direction _CD_, which is
clearly parallel to its original direction. Hence, when we view
objects through the window, we see them slightly displaced in
position, but otherwise unchanged. The deviation or displacement
caused by glass as thin as window panes is too slight to be noticed,
and we are not conscious that objects are out of position.
[Illustration: FIG. 67.--Objects looked at through a window pane seem
to be in their natural place.]
111. Chandelier Crystals and Prisms. When a ray of light passes
through plane glass, like a window pane, it is shifted somewhat, but
its direction does not change; that is, the emergent ray is parallel
to the incident ray. But when a beam of light passes through a
triangular glass prism, such as a chandelier crystal, its direction is
greatly changed, and an object viewed through a prism is seen quite
out of its true position.
Whenever light passes through a prism, it is bent toward the base of
the prism, or toward the thick portion of the prism, and emerges from
the prism in quite a different direction from that in which it entered
(Fig. 68). Hence, when an object is looked at through a prism, it is
seen quite out of place. In Figure 68, the candle seems to be at _S_,
while in reality it is at _A_.
[Illustration: FIG. 68.--When looked at through the prism, _A_ seems
to be at _S_.]
112. Lenses. If two prisms are arranged as in Figure 69, and two
parallel rays of light fall upon the prisms, the beam _A_ will be bent
downward toward the thickened portion of the prism, and the beam _B_
will be bent upward toward the thick portion of the prism, and after
passing through the prism the two rays will intersect at some point
_F_, called a focus.
[Illustration: FIG. 69.--Rays of light are converged and focused at
_F_.]
If two prisms are arranged as in Figure 70, the ray _A_ will be
refracted upward toward the thick end, and the ray _B_ will be
refracted downward toward the thick end; the two rays, on emerging,
will therefore be widely separated and will not intersect.
[Illustration: FIG. 70.--Rays of light are diverged and do not come to
any real focus.]
Lenses are very similar to prisms; indeed, two prisms placed as in
Figure 69, and rounded off, would make a very good convex lens. A lens
is any transparent material, but usually glass, with one or both sides
curved. The various types of lenses are shown in Figure 71.
[Illustration: FIG. 71.--The different types of lenses.]
The first three types focus parallel rays at some common point _F_, as
in Figure 69. Such lenses are called convex or converging lenses. The
last three types, called concave lenses, scatter parallel rays so that
they do not come to a focus, but diverge widely after passage through
the lens.
113. The Shape and Material of a Lens. The main or principal focus
of a lens, that is, the point at which rays parallel to the base line
_AB_ meet (Fig. 71), depends upon the shape of the lens. For example,
a thick lens, such as _A_ (Fig. 72), focuses the rays very near to the
lens; _B_, which is not so thick, focuses the rays at a greater
distance from the lens; and _C_, which is a very thin lens, focuses
the rays at a considerable distance from the lens. The distance of the
principal focus from the lens is called the focal length of the lens,
and from the diagrams we see that the more convex the lens, the
shorter the focal length.
[Illustration: FIG. 72.--The more curved the lens, the shorter the
focal length, and the nearer the focus is to the lens.]
The position of the principal focus depends not only on the shape of
the lens, but also on the refractive power of the material composing
the lens. A lens made of ice would not deviate the rays of light so
much as a lens of similar shape composed of glass. The greater the
refractive power of the lens, the greater the bending, and the nearer
the principal focus to the lens.
There are many different kinds of glass, and each kind of glass
refracts the light differently. Flint glass contains lead; the lead
makes the glass dense, and gives it great refractive power, enabling
it to bend and separate light in all directions. Cut glass and toilet
articles are made of flint glass because of the brilliant effects
caused by its great refractive power, and imitation gems are commonly
nothing more than polished flint glass.
114. How Lenses Form Images. Suppose we place an arrow, _A_, in
front of a convex lens (Fig. 73). The ray _AC_, parallel to the
principal axis, will pass through the lens and emerge as _DE_. The ray
is always bent toward the thick portion of the lens, both at its
entrance into the lens and its emergence from the lens.
[Illustration: FIG. 73.--The image is larger than the object. By means
of a lens, a watchmaker gets an enlarged image of the dust which clogs
the wheels of his watch.]
In Section 105, we saw that two rays determine the position of any
point of our image; hence in order to locate the image of the top of
the arrow, we need to consider but one more ray from the top of the
object. The most convenient ray to choose would be one passing through
_O_, the optical center of the lens, because such a ray passes through
the lens unchanged in direction, as is clear from Figure 74. The point
where _AC_ and _AO_ meet after refraction will be the position of the
top of the arrow. Similarly it can be shown that the center of the
arrow will be at the point _T_, and we see that the image is larger
than the object. This can be easily proved experimentally. Let a
convex lens be placed near a candle (Fig. 75); move a paper screen
back and forth behind the lens; for some position of the screen a
clear, enlarged image of the candle will be made.
[Illustration: FIG. 74.--Rays above _O_ are bent downward, those below
_O_ are bent upward, and rays through _O_ emerge from the lens
unchanged in direction.]
If the candle or arrow is placed in a new position, say at _MA_ (Fig.
76), the image formed is smaller than the object, and is nearer to the
lens than it was before. Move the lens so that its distance from the
candle is increased, and then find the image on a piece of paper. The
size and position of the image depend upon the distance of the object
from the lens (Fig. _77_). By means of a lens one can easily get on a
visiting card a picture of a distant church steeple.
[Illustration: FIG. 75.--The lens is held in such a position that the
image of the candle is larger than the object.]
[Illustration: FIG. 76.--The image is smaller than the object.]
115. The Value of Lenses. If it were not for the fact that a lens
can be held at such a distance from an object as to make the image
larger than the object, it would be impossible for the lens to assist
the watchmaker in locating the small particles of dust which clog the
wheels of the watch. If it were not for the opposite fact--that a lens
can be held at such a distance from the object as to make an image
smaller than the object, it would be impossible to have a photograph
of a tall tree or building unless the photograph were as large as the
tree itself. When a photographer takes a photograph of a person or a
tree, he moves his camera until the image formed by the lens is of the
desired size. By bringing the camera (really the lens of the camera)
near, we obtain a large-sized photograph; by increasing the distance
between the camera and the object, a smaller photograph is obtained.
The mountain top may be so far distant that in the photograph it will
not appear to be greater than a small stone.
[Illustration: FIG. 77.--The lens is placed in such a position that
the image is about the same size as the object.]
Many familiar illustrations of lenses, or curved refracting surfaces,
and their work, are known to all of us. Fish globes magnify the fish
that swim within. Bottles can be so shaped that they make the olives,
pickles, and peaches that they contain appear larger than they really
are. The fruit in bottles frequently seems too large to have gone
through the neck of the bottle. The deception is due to refraction,
and the material and shape of the bottle furnish a sufficient
explanation.
By using combinations of two or more lenses of various kinds, it is
possible to have an image of almost any desired size, and in
practically any desired position.
116. The Human Eye. In Section 114, we obtained on a movable screen,
by means of a simple lens, an image of a candle. The human eye
possesses a most wonderful lens and screen (Fig. 78); the lens is
called the crystalline lens, and the screen is called the retina. Rays
of light pass from the object through the pupil _P_, go through the
crystalline lens _L_, where they are refracted, and then pass onward
to the retina _R_, where they form a distinct image of the object.
[Illustration: FIG. 78.--The eye.]
We learned in Section 114 that a change in the position of the object
necessitated a change in the position of the screen, and that every
time the object was moved the position of the screen had to be altered
before a clear image of the object could be obtained. The retina of
the eye cannot be moved backward and forward, as the screen was, and
the crystalline lens is permanently located directly back of the iris.
How, then, does it happen that we can see clearly both near and
distant objects; that the printed page which is held in the hand is
visible at one second, and that the church spire on the distant
horizon is visible the instant the eyes are raised from the book? How
is it possible to obtain on an immovable screen by means of a simple
lens two distinct images of objects at widely varying distances?
The answer to these questions is that the crystalline lens changes
shape according to need. The lens is attached to the eye by means of
small muscles, _m_, and it is by the action of these muscles that the
lens is able to become small and thick, or large and thin; that is, to
become more or less curved. When we look at near objects, the muscles
act in such a way that the lens bulges out, and becomes thick in the
middle and of the right curvature to focus the near object upon the
screen. When we look at an object several hundred feet away, the
muscles change their pull on the lens and flatten it until it is of
the proper curvature for the new distance. The adjustment of the
muscles is so quick and unconscious that we normally do not experience
any difficulty in changing our range of view. The ability of the eye
to adjust itself to varying distances is called accommodation. The
power of adjustment in general decreases with age.
117. Farsightedness and Nearsightedness. A farsighted person is one
who cannot see near objects so distinctly as far objects, and who in
many cases cannot see near objects at all. The eyeball of a farsighted
person is very short, and the retina is too close to the crystalline
lens. Near objects are brought to a focus behind the retina instead of
on it, and hence are not visible. Even though the muscles of
accommodation do their best to bulge and thicken the lens, the rays of
light are not bent sufficiently to focus sharply on the retina. In
consequence objects look blurred. Farsightedness can be remedied by
convex glasses, since they bend the light and bring it to a closer
focus. Convex glasses, by bending the rays and bringing them to a
nearer focus, overbalance a short eyeball with its tendency to focus
objects behind the retina.
[Illustration: FIG. 79.--The farsighted eye.]
[Illustration: FIG. 80.--The defect is remedied by convex glasses.]
A nearsighted person is one who cannot see objects unless they are
close to the eye. The eyeball of a nearsighted person is very wide,
and the retina is too far away from the crystalline lens. Far objects
are brought to a focus in front of the retina instead of on it, and
hence are not visible. Even though the muscles of accommodation do
their best to pull out and flatten the lens, the rays are not
separated sufficiently to focus as far back as the retina. In
consequence objects look blurred. Nearsightedness can be remedied by
wearing concave glasses, since they separate the light and move the
focus farther away. Concave glasses, by separating the rays and making
the focus more distant, overbalance a wide eyeball with its tendency
to focus objects in front of the retina.
[Illustration: FIG. 81.--The nearsighted eye. The defect is remedied
by concave glasses.]
118. Headache and Eyes. Ordinarily the muscles of accommodation
adjust themselves easily and quickly; if, however, they do not,
frequent and severe headaches occur as a result of too great muscular
effort toward accommodation. Among young people headaches are
frequently caused by over-exertion of the crystalline muscles. Glasses
relieve the muscles of the extra adjustment, and hence are effective
in eliminating this cause of headache.
An exact balance is required between glasses, crystalline lens, and
muscular activity, and only those who have studied the subject
carefully are competent to treat so sensitive and necessary a part of
the body as the eye. The least mistake in the curvature of the
glasses, the least flaw in the type of glass (for example, the kind of
glass used), means an improper focus, increased duty for the muscles,
and gradual weakening of the entire eye, followed by headache and
general physical discomfort.
119. Eye Strain. The extra work which is thrown upon the nervous
system through seeing, reading, writing, and sewing with defective
eyes is recognized by all physicians as an important cause of disease.
The tax made upon the nervous system by the defective eye lessens the
supply of energy available for other bodily use, and the general
health suffers. The health is improved when proper glasses are
prescribed.
Possibly the greatest danger of eye strain is among school children,
who are not experienced enough to recognize defects in sight. For this
reason, many schools employ a physician who examines the pupils' eyes
at regular intervals.
The following general precautions are worth observing:--
1. Rest the eyes when they hurt, and as far as possible do close work,
such as writing, reading, sewing, wood carving, etc., by daylight.
2. Never read in a very bright or a very dim light.
3. If the light is near, have it shaded.
4. Do not rub the eyes with the fingers.
5. If eyes are weak, bathe them in lukewarm water in which a pinch of
borax has been dissolved.