CHAPTER X.
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.
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.
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.
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.
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.
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 | +---------------+-----------+
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.
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.
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.
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.
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.
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.