REFLECTION.
Light may be reflected from opaque or transparent bodies such as glass.
In the case of transparent bodies, the reflected rays are not noticeable
unless the ground behind the reflecting body is dark. If there is much
light behind a pane of glass, for instance, the pupil of the eye will be
partially closed and not be able to see the faint light which is
reflected. As we gradually darken the space behind the glass, the image
begins to appear more and more distinct, partly from contrast with the
dark background and partly on account of the increased opening of the
pupil. This can be readily noticed if some evening out of a
dimly-lighted room we look at some object just discernible. If we then
turn on the light suddenly, the object will at once disappear but
reflections will appear in the glass where there were none before.
The reflections from clear glass are much stronger at an angle than when
the rays are thrown straight back. This can be seen by placing any
object directly in front of a pane of glass with a dark background. If
we place the eye so as to receive only those rays which are reflected
directly back, we shall obtain but a weak reflection. If, however, we
place the object a little to one side and stand close to the glass, we
shall see the object almost as plainly as in a regular mirror.
A ray of light is always reflected at exactly the same angle at which
it strikes, the reflecting body; that is, the angle of incidence is
equal and opposite to the angle of reflection. This can be illustrated
by Figure 64. If a mirror be attached to the pointer in the position
shown at an angle of exactly ninety degrees and a beam of light be
allowed to enter through the slit at the top, it will be reflected back
exactly to the spot at which it entered. If we then turn the pointer
slightly, we shall notice that the reflection of the beam of light moves
twice as fast as the pointer and, when the pointer occupies the position
indicated by broken lines, the light will be reflected at right angles
to the line along which it enters. If the mirror is turned still more,
the same law will hold; so that, if the mirror were turned through an
angle of nearly ninety degrees, the reflected beam of light would in the
same space of time make an angle of nearly one hundred eighty degrees.
[Illustration: FIGURE 64.]
Reflected light results in the formation of images in mirrors and other
reflecting bodies and, by bearing in mind the law of reflection given
above, we can readily explain how these images are formed and the manner
in which they appear to us.
[Illustration: FIGURE 65.]
Let _N_, Figure 65 be an object in front of the mirror. The only rays
that are reflected back to the eye are those that strike the mirror at
the proper angle. All others are wasted with reference to the
particular position of the eye. If the eye and the object reflected are
equally distant from the mirror, we need but draw a line at right angles
to the mirror and half way between the eye and the object and, from
these two, draw lines to the point at which the perpendicular line
strikes the mirror. The two lines thus drawn will give us the path of
the incident and the reflected rays. The image will appear to lie in the
direction from which the reflected ray comes and as far behind the
mirror as the object is in front of it. If the eye and the object to be
reflected are not equally distant from the mirror, it is more difficult
to find the paths of the rays and it simplifies matters very much to use
the following construction: Draw a line from the object before the
mirror at right angles to the mirror and extend it behind the mirror as
far as the object is in front of it. From this point behind the mirror,
draw another line to the eye. By drawing a third line from the object to
the point in the mirror where this line, from back of the mirror to the
eye, crosses it, we shall obtain the paths of the rays and the position
of the image in the mirror. The image will exist in the mirror at the
point where the reflected and incident rays meet but will have the
appearance of lying some distance behind the mirror. This is illustrated
in Figure 65, _N_ being the object reflected and _M_ the apparent
position of the image to the eyes as located in the cut.
[Illustration: FIGURE 66.]
[Illustration: FIGURE 67.]
[Illustration: FIGURE 68.]
In Figures 66 and 67 the same construction is used to show the
appearance of arrows as they are reflected from a mirror to the eye.
Objects standing erect over horizontal mirrors or arranged at right
angles to mirrors and looked at, as in Figure 68, always appear
inverted. This can be noticed in quiet ponds of clear water which give
reflections of trees and other objects. Figure 68 shows two arrows, one
horizontal, the other vertical; by the construction in the figure one
appears inverted, the other not. If the arrow were placed in the
position indicated by broken lines, the eye would see only the butt. If
the arrow were placed a little nearer the horizontal, it would appear in
its natural position; if a little more vertical, it would appear
inverted in the mirror.
[Illustration: FIGURE 69.]
All objects seen in mirrors are reversed with reference to right and
left. A pocket on the left side of a person facing a mirror will appear
to be on the right side. Printed matter held before a mirror will appear
just as it would if seen through the paper from the back side and will
have to be read from right to left.
[Illustration: FIGURE 70.]
[Illustration: FIGURE 71.]
[Illustration: FIGURE 72.]
If an object be placed between two parallel mirrors as _B_, Figure 69,
there will be a vast number of reflections visible at the point _D_.
Several reflections of _B_ will come to the eye in the manner indicated
but there will be a large number of additional reflections. If the
mirrors are exactly parallel and absolutely smooth, the number of
reflections would theoretically be infinite. At each reflection,
however, some light is absorbed and some diffused so that many of the
reflections are not discernible. Two mirrors set opposite each other
will also give many reflections of each other as indicated in Figure 70.
The images seen in parallel mirrors all appear arranged in straight
lines on both sides, as indicated in Figure 69. If now one of the
mirrors be inclined so as to form an angle with the other, the long line
of images will seem to become curved and finally lie in a circle. If the
mirrors be placed at right angles to each other, as in Figure 71, there
will be three reflections of the object _C_ visible and these will
reach the eye by the paths shown. If the mirrors be placed at an angle
of sixty degrees to each other, five images will appear as shown in
Figure 72, in which _A_ is the object being reflected.
The following tabulation shows the number of images obtainable at
different angles between the mirrors.
+---------------+-----------+
| Angle between | Number of |
| mirrors | images |
+---------------+-----------+
| 90 degrees | 3 |
| 72 degrees | 4 |
| 60 degrees | 5 |
| 45 degrees | 7 |
| 30 degrees | 11 |
+---------------+-----------+
[Illustration: FIGURE 73.]
Instead of being plain, mirrors may be either _concave_ or _convex_. A
concave mirror is hollowed out in conformity with a small section of the
surface of a sphere. If a piece of glass be cut out of a hollow sphere,
the inner side of it will show the surface of a concave, and the outer
side, the surface of a convex mirror. A section of a concave mirror is
shown in Figure 73. _C_ is the center of curvature and any line drawn
from the surface of the mirror to this center is at right angles, or
normal, to the curvature of the mirror. A ray of light emanating from
this center will be reflected straight back to it. If the source of
light be moved a little nearer to the mirror, the light reflected will
be spread out more and come to a focus farther back from the glass; if
it be moved farther back from the glass, the rays will be focused nearer
the mirror. Thus if a light be placed at _A_, its rays will be focused
at _D_ and a light placed at _D_ will focus at _A_. This can be seen by
the lines which represent the rays of light. The two points at which a
source of light will thus focus are known as the _conjugate foci_ of the
mirror.
If such a mirror receives parallel rays of light, they will be reflected
and come to a focus at a point midway between the mirror and the center
of curvature. This point is known as the _principal focus_ of the
mirror, and the distance between it and the mirror is called the _focal
length_ of the mirror. A source of light placed at this point will throw
out parallel rays from the mirror. If the light be moved closer to the
mirror, the reflected rays will spread out; while if moved farther away,
the light will come to a focus at some distant point, as shown above.
Figure 74 can be used to illustrate the manner in which a concave mirror
reflects the light from an object placed before it. From the upper point
of the large arrow, rays of light emanate in all directions. All that
strike the face of the mirror are thrown to a certain point which can be
found by tracing out the lines, using the small arrows as guides. At
this point will appear the image of the top of the arrow. It will be
noted that it is inverted. The rays from the lower part of the arrow
are of course all reflected in the same manner.
[Illustration: FIGURE 74.]
With mirrors of this kind, the position of the object with reference to
the focal length and center of curvature is of great importance. If the
object be placed in the position shown as the image in Figure 74, the
image will appear as though it were in place of the object; it will be
much enlarged and also inverted. If the object is placed between the
principal focus and the mirror, it will appear to lie behind the mirror
as shown in Figure 75. In this case it will not be inverted.
[Illustration: FIGURE 75.]
When concave mirrors forming large sections of spheres are used, the
rays reflected from the outer edges will not all meet exactly at the
focal point. There will then be a somewhat fuzzy image formed. This is
illustrated in Figure 76. In order to obtain a perfectly clear and
distinct image, only the central part of concave mirrors should be used.
[Illustration: FIGURE 76.]
Convex mirrors are not much used. Sometimes glass spheres are set up to
show miniature reflections of scenery; convex mirrors are also found in
the lobbies of theaters and in places of amusement to amuse the patrons
with the caricatures of themselves reflected in them.
[Illustration: FIGURE 77.]
All of the rays that strike a convex mirror are reflected back in such a
manner that they seem to come from a common point behind the mirror.
This is shown in Figure 77. The center of curvature here is behind the
mirror but the paths of the various rays can be determined as before
explained. Thus we shall find that every ray, striking the mirror from a
certain point, is reflected back in a direction which gives it the
appearance of coming from a certain point behind the mirror. Two such
points are shown in Figure 77.
[Illustration: FIGURE 78.]
In Figure 78 we have drawn the arrow and the image it would produce in
the mirror. If the mirror forms a section of a sphere, the object
reflected will appear reduced in size in all directions. If the mirror
forms merely a section of a cylinder, a person standing in front of it
will appear very much shorter than natural but of full width thus
presenting a ridiculous appearance. Convex and concave mirrors are often
combined and if properly set, a person standing in front of one may see
himself either very much elongated or shortened.