OPTICS.
Lenses--The image cast by a convex lens--Focus--Relative position
of object and lens--Correction of lenses for colour--Spherical
aberration--Distortion of image--The human eye--The use of
spectacles--The blind spot.
Light is a third form of that energy of which we have already treated
two manifestations--heat and electricity. The distinguishing
characteristic of ether light-waves is their extreme rapidity of
vibration, which has been calculated to range from 700 billion movements
per second for violet rays to 400 billion for red rays.
If a beam of white light be passed through a prism it is resolved into
the seven visible colours of the spectrum--violet, indigo, blue, green,
yellow, orange, and red--in this order. The human eye is most sensitive
to the yellow-red rays, a photographic plate to the green-violet rays.
All bodies fall into one of two classes--(1) _Luminous_--that is, those
which are a _source_ of light, such as the sun, a candle flame, or a
red-hot coal; and (2) _non-luminous_, which become visible only by
virtue of light which they receive from other bodies and reflect to our
eyes.
THE PROPAGATION OF LIGHT.
Light naturally travels in a straight line. It is deflected only when it
passes from one transparent medium into another--for example, from air
to water--and the mediums are of different densities. We may regard the
surface of a visible object as made up of countless points, from each of
which a diverging pencil of rays is sent off through the ether.
LENSES.
If a beam of light encounters a transparent glass body with non-parallel
sides, the rays are deflected. The direction they take depends on the
shape of the body, but it may be laid down as a rule that they are bent
toward the thicker part of the glass. The common burning-glass is well
known to us. We hold it up facing the sun to concentrate all the heat
rays that fall upon it into one intensely brilliant spot, which speedily
ignites any inflammable substance on which it may fall (Fig. 103). We
may imagine that one ray passes from the centre of the sun through the
centre of the glass. This is undeflected; but all the others are bent
towards it, as they pass through the thinner parts of the lens.
[Illustration: FIG. 103.--Showing how a burning-glass concentrates the
heat rays which fall upon it.]
It should be noted here that _sunlight_, as we call it, is accompanied
by heat. A burning-glass is used to concentrate the _heat_ rays, not the
_light_ rays, which, though they are collected too, have no igniting
effect.
In photography we use a lens to concentrate light rays only. Such heat
rays as may pass through the lens with them are not wanted, and as they
have no practical effect are not taken any notice of. To be of real
value, a lens must be quite symmetrical--that is, the curve from the
centre to the circumference must be the same in all directions.
There are six forms of simple lenses, as given in Fig. 104. Nos. 1 and
2 have one flat and one spherical surface. Nos. 3, 4, 5, 6 have two
spherical surfaces. When a lens is thicker at the middle than at the
sides it is called a _convex_ lens; when thinner, a _concave_ lens. The
names of the various shapes are as follows:--No. 1, plano-convex; No. 2,
plano-concave; No. 3, double convex; No. 4, double concave; No. 5,
meniscus; No. 6, concavo-convex. The thick-centre lenses, as we may term
them (Nos. 1, 3, 5), _concentrate_ a pencil of rays passing through
them; while the thin-centre lenses (Nos. 2, 4, 6) _scatter_ the rays
(see Fig. 105).
[Illustration: FIG. 104.--Six forms of lenses.]
THE CAMERA.
[Illustration: FIG. 105.]
[Illustration: FIG. 106.]
We said above that light is propagated in straight lines. To prove this
is easy. Get a piece of cardboard and prick a hole in it. Set this up
some distance away from a candle flame, and hold behind it a piece of
tissue paper. You will at once perceive a faint, upside-down image of
the flame on the tissue. Why is this? Turn for a moment to Fig. 106,
which shows a "pinhole" camera in section. At the rear is a ground-glass
screen, B, to catch the image. Suppose that A is the lowest point of the
flame. A pencil of rays diverging from it strikes the front of the
camera, which stops them all except the one which passes through the
hole and makes a tiny luminous spot on B, _above_ the centre of the
screen, though A is below the axis of the camera. Similarly the tip of
the flame (above the axis) would be represented by a dot on the screen
below its centre. And so on for all the millions of points of the flame.
If we were to enlarge the hole we should get a brighter image, but it
would have less sharp outlines, because a number of rays from every
point of the candle would reach the screen and be jumbled up with the
rays of neighbouring pencils. Now, though a good, sharp photograph may
be taken through a pinhole, the time required is so long that
photography of this sort has little practical value. What we want is a
large hole for the light to enter the camera by, and yet to secure a
distinct image. If we place a lens in the hole we can fulfil our wish.
Fig. 107 shows a lens in position, gathering up a number of rays from a
point, A, and focussing them on a point, B. If the lens has 1,000 times
the area of the pinhole, it will pass 1,000 times as many rays, and the
image of A will be impressed on a sensitized photographic plate 1,000
times more quickly.
[Illustration: FIG. 107.]
THE IMAGE CAST BY A CONVEX LENS.
Fig. 108 shows diagrammatically how a convex lens forms an image. From A
and B, the extremities of the object, a simple ray is considered to pass
through the centre of the lens. This is not deflected at all. Two other
rays from the same points strike the lens above and below the centre
respectively. These are bent inwards and meet the central rays, or come
to a focus with them at A^1 and B^1. In reality a countless number
of rays would be transmitted from every point of the object and
collected to form the image.
[Illustration: FIG. 108.--Showing how an image is cast by a convex
lens.]
FOCUS.
We must now take special notice of that word heard so often in
photographic talk--"focus." What is meant by the focus or focal length
of a lens? Well, it merely signifies the distance between the optical
centre of the lens and the plane in which the image is formed.
[Illustration: FIG. 109.]
We must here digress a moment to draw attention to the three simple
diagrams of Fig. 109. The object, O, in each case is assumed to be to
the right of the lens. In the topmost diagram the object is so far away
from the lens that all rays coming from a single point in it are
practically parallel. These converge to a focus at F. If the distance
between F and the centre of the lens is six inches, we say that the
lens has a six-inch focal length. The focal length of a lens is judged
by the distance between lens and image when the object is far away. To
avoid confusion, this focal length is known as the _principal_ focus,
and is denoted by the symbol f. In the middle diagram the object is
quite near the lens, which has to deal with rays striking its nearer
surface at an acuter angle than before (reckoning from the centre). As
the lens can only deflect their path to a fixed degree, they will not,
after passing the lens, come together until they have reached a point,
F^1, further from the lens than F. The nearer we approach O to the
lens, the further away on the other side is the focal point, until a
distance equal to that of F from the lens is reached, when the rays
emerge from the glass in a parallel pencil. The rays now come to a focus
no longer, and there can be no image. If O be brought nearer than the
focal distance, the rays would _diverge_ after passing through the lens.
RELATIVE POSITIONS OF OBJECT AND IMAGE.
[Illustration: FIG. 110.--Showing how the position of the image alters
relatively to the position of the object.]
From what has been said above we deduce two main conclusions--(1.) The
nearer an object is brought to the lens, the further away from the lens
will the image be. (2.) If the object approaches within the principal
focal distance of the lens, no image will be cast by the lens. To make
this plainer we append a diagram (Fig. 110), which shows five positions
of an object and the relative positions of the image (in dotted lines).
First, we note that the line A B, or A B^1, denotes the principal
focal length of the lens, and A C, or A C^1, denotes twice the focal
length. We will take the positions in order:--
_Position I._ Object further away than 2_f_. Inverted image _smaller_
than object, at distance somewhat exceeding _f_.
_Position II._ Object at distance = 2_f_. Inverted image at distance =
2_f_, and of size equal to that of object.
_Position III_ Object nearer than 2_f_. Inverted image further away than
2_f_; _larger_ than the object.
_Position IV._ Object at distance = _f_. As rays are parallel after
passing the lens _no_ image is cast.
_Position V._ Object at distance less than _f_. No real image--that is,
one that can be caught on a focussing screen--is now given by the lens,
but a magnified, erect, _virtual_ image exists on the same side of the
lens as the object.
We shall refer to _virtual_ images at greater length presently. It is
hoped that any reader who practises photography will now understand why
it is necessary to rack his camera out beyond the ordinary focal
distance when taking objects at close quarters. From Fig. 110 he may
gather one practically useful hint--namely, that to copy a diagram,
etc., full size, both it and the plate must be exactly 2_f_ from the
optical centre of the lens. And it follows from this that the further he
can rack his camera out beyond 2_f_ the greater will be the possible
enlargement of the original.
CORRECTION OF LENSES FOR COLOUR.
We have referred to the separation of the spectrum colours of white
light by a prism. Now, a lens is one form of prism, and therefore sorts
out the colours. In Fig. 111 we assume that two parallel red rays and
two parallel violet rays from a distant object pass through a lens. A
lens has most bending effect on violet rays and least on red, and the
other colours of the spectrum are intermediately influenced. For the
sake of simplicity we have taken the two extremes only. You observe that
the point R, in which the red rays meet, is much further from the lens
than is V, the meeting-point of the violet rays. A photographer very
seldom has to take a subject in which there are not objects of several
different colours, and it is obvious that if he used a simple lens like
that in Fig. 111 and got his red objects in good focus, the blue and
green portions of his picture would necessarily be more or less out of
focus.
[Illustration: FIG. 111.]
[Illustration: FIG. 112.]
This defect can fortunately be corrected by the method shown in Fig.
112. A _compound_ lens is needed, made up of a _crown_ glass convex
element, B, and a concave element, A, of _flint_ glass. For the sake of
illustration the two parts are shown separated; in practice they would
be cemented together, forming one optical body, thicker in the centre
than at the edges--a meniscus lens in fact, since A is not so concave as
B is convex. Now, it was discovered by a Mr. Hall many years ago that if
white light passed through two similar prisms, one of flint glass the
other of crown glass, the former had the greater effect in separating
the spectrum colours--that is, violet rays were bent aside more suddenly
compared with the red rays than happened with the crown-glass prism.
Look at Fig. 112. The red rays passing through the flint glass are but
little deflected, while the violet rays turn suddenly outwards. This is
just what is wanted, for it counteracts the unequal inward refraction
by B, and both sets of rays come to a focus in the same plane. Such a
lens is called _achromatic_, or colourless. If you hold a common
reading-glass some distance away from large print you will see that the
letters are edged with coloured bands, proving that the lens is not
achromatic. A properly corrected photographic lens would not show these
pretty edgings. Colour correction is necessary also for lenses used in
telescopes and microscopes.
SPHERICAL ABERRATION.
A lens which has been corrected for colour is still imperfect. If rays
pass through all parts of it, those which strike it near the edge will
be refracted more than those near the centre, and a blurred focus
results. This is termed _spherical aberration_. You will be able to
understand the reason from Figs. 113 and 114. Two rays, A, are parallel
to the axis and enter the lens near the centre (Fig. 113). These meet in
one plane. Two other rays, B, strike the lens very obliquely near the
edge, and on that account are both turned sharply upwards, coming to a
focus in a plane nearer the lens than A. If this happened in a camera
the results would be very bad. Either A or B would be out of focus. The
trouble is minimized by placing in front of the lens a plate with a
central circular opening in it (denoted by the thick, dark line in Fig.
114). The rays B of Fig. 113 are stopped by this plate, which is
therefore called a _stop_. But other rays from the same point pass
through the hole. These, however, strike the lens much more squarely
above the centre, and are not unduly refracted, so that they are brought
to a focus in the same plane as rays A.
[Illustration: FIG. 113.]
[Illustration: FIG. 114.]
DISTORTION OF IMAGE.
[Illustration: FIG. 115.--Section of a rectilinear lens.]
The lens we have been considering is a single meniscus, such as is used
in landscape photography, mounted with the convex side turned towards
the inside of the camera, and having the stop in front of it. If you
possess a lens of this sort, try the following experiment with it. Draw
a large square on a sheet of white paper and focus it on the screen. The
sides instead of being straight bow outwards: this is called _barrel_
distortion. Now turn the lens mount round so that the lens is outwards
and the stop inwards. The sides of the square will appear to bow towards
the centre: this is _pin-cushion_ distortion. For a long time opticians
were unable to find a remedy. Then Mr. George S. Cundell suggested that
_two_ meniscus lenses should be used in combination, one on either side
of the stop, as in Fig 115. Each produces distortion, but it is
counteracted by the opposite distortion of the other, and a square is
represented as a square. Lenses of this kind are called _rectilinear_,
or straight-line producing.
We have now reviewed the three chief defects of a lens--chromatic
aberration, spherical aberration, and distortion--and have seen how they
may be remedied. So we will now pass on to the most perfect of cameras,
THE HUMAN EYE.
The eye (Fig. 116) is nearly spherical in form, and is surrounded
outside, except in front, by a hard, horny coat called the _sclerotica_
(S). In front is the _cornea_ (A), which bulges outwards, and acts as a
transparent window to admit light to the lens of the eye (C). Inside the
sclerotica, and next to it, comes the _choroid_ coat; and inside that
again is the _retina_, or curved focussing screen of the eye, which may
best be described as a network of fibres ramifying from the optic nerve,
which carries sight sensations to the brain. The hollow of the ball is
full of a jelly-like substance called the _vitreous humour_; and the
cavity between the lens and the cornea is full of water.
We have already seen that, in focussing, the distance between lens and
image depends on the distance between object and lens. Now, the retina
cannot be pushed nearer to or pulled further away from its lens, like
the focussing screen of a camera. How, then, is the eye able to focus
sharply objects at distances varying from a foot to many miles?
[Illustration: FIG. 116.--Section of the human eye.]
As a preliminary to the answer we must observe that the more convex a
lens is, the shorter is its focus. We will suppose that we have a box
camera with a lens of six-inch focus fixed rigidly in the position
necessary for obtaining a sharp image of distant objects. It so happens
that we want to take with it a portrait of a person only a few feet from
the lens. If it were a bellows camera, we should rack out the back or
front. But we cannot do this here. So we place in front of our lens a
second convex lens which shortens its principal focus; so that _in
effect_ the box has been racked out sufficiently.
Nature, however, employs a much more perfect method than this. The eye
lens is plastic, like a piece of india-rubber. Its edges are attached to
ligaments (L L), which pull outwards and tend to flatten the curve of
its surfaces. The normal focus is for distant objects. When we read a
book the eye adapts itself to the work. The ligaments relax and the lens
decreases in diameter while thickening at the centre, until its
curvature is such as to focus all rays from the book sharply on the
retina. If we suddenly look through the window at something outside, the
ligaments pull on the lens envelope and flatten the curves.
This wonderful lens is achromatic, and free from spherical aberration
and distortion of image. Nor must we forget that it is aided by an
automatic "stop," the _iris_, the central hole of which is named the
_pupil_. We say that a person has black, blue, or gray eyes according to
the colour of the iris. Like the lens, the iris adapts itself to all
conditions, contracting when the light is strong, and opening when the
light is weak, so that as uniform an amount of light as conditions allow
may be admitted to the eye. Most modern camera lenses are fitted with
adjustable stops which can be made larger or smaller by twisting a ring
on the mount, and are named "iris" stops. The image of anything seen is
thrown on the retina upside down, and the brain reverses the position
again, so that we get a correct impression of things.
THE USE OF SPECTACLES.
[Illustration: FIG. 117_a_.]
[Illustration: FIG. 117_b_.]
[Illustration: FIG. 118_a_.]
[Illustration: FIG. 118_b_.]
The reader will now be able to understand without much trouble the
function of a pair of spectacles. A great many people of all ages suffer
from short-sight. For one reason or another the distance between lens
and retina becomes too great for a person to distinguish distant objects
clearly. The lens, as shown in Fig 117_a_, is too convex--has its
minimum focus too short--and the rays meet and cross before they reach
the retina, causing general confusion of outline. This defect is simply
remedied by placing in front of the eye (Fig. 117_b_) a _concave_ lens,
to disperse the rays somewhat before they enter the eye, so that they
come to a focus on the retina. If a person's sight is thus corrected for
distant objects, he can still see near objects quite plainly, as the
lens will accommodate its convexity for them. The scientific term for
short-sight is _myopia_. Long-sight, or _hypermetropia_, signifies that
the eyeball is too short or the lens too flat. Fig. 118_a_ represents
the normal condition of a long-sighted eye. When looking at a distant
object the eye thickens slightly and brings the focus forward into the
retina. But its thickening power in such an eye is very limited, and
consequently the rays from a near object focus behind the retina. It is
therefore necessary for a long-sighted person to use _convex_ spectacles
for reading the newspaper. As seen in Fig. 118_b_, the spectacle lens
concentrates the rays before they enter the eye, and so does part of the
eye's work for it.
Returning for a moment to the diagram of the eye (Fig. 116), we notice a
black patch on the retina near the optic nerve. This is the "yellow
spot." Vision is most distinct when the image of the object looked at is
formed on this part of the retina. The "blind spot" is that point at
which the optic nerve enters the retina, being so called from the fact
that it is quite insensitive to light. The finding of the blind spot is
an interesting little experiment. On a card make a large and a small
spot three inches apart, the one an eighth, the other half an inch in
diameter. Bring the card near the face so that an eye is exactly
opposite to each spot, and close the eye opposite to the smaller. Now
direct the other eye to this spot and you will find, if the card be
moved backwards and forwards, that at a certain distance the large spot,
though many times larger than its fellow, has completely vanished,
because the rays from it enter the open eye obliquely and fall on the
"blind spot."