Popular Science Monthly/Volume 5/May 1874/The Crooked Courses of Light


AN article in the April Monthly explained the formation of luminous images upon the principle that light moves in straight lines through any uniform transparent medium; but at the same time no agency in Nature illustrates in so many ways its capability of being turned from a direct course. It may be thrown back by surfaces either directly in its own path, or at all possible angles, and it may be warped out of its course in various degrees as it passes through bodies, although in all cases the change of direction is governed by inflexible laws. The throwing back of rays from surfaces is known as the reflection of light; the bending or the fracture of the ray as it traverses a body is called the refraction of light.

The principle of reflection is illustrated in Fig. 1, in which a beam of the sun's rays enters through the shutter of a dark room, strikes upon a polished plane surface, and is reflected across the room in an opposite direction. The entering beam, A B, is called the incident ray. The vertical line, B D, is termed the normal and the beam B C,

Fig. 1.

Illustration of the Reflection of light

the reflected ray. The angle A D B, contained between the incident ray and the normal, is termed the angle of incidence; and the angle C B D, contained between the corresponding reflected ray and the normal, is called the angle of reflection. The reflection of light by polished surfaces, as in this case, is governed by two laws: 1. The incident ray, the normal, and the reflected ray, are always in the same plane; and, 2. The angle of incidence is always equal to the angle of reflection.

Fig. 2.

Image of a Candle in a Looking-Glass.

This is an example of what is known as regular reflection, but there is another kind of reflection in virtue of which bodies, when illuminated, throw back the light in all directions, and this is known as irregular reflection or diffusion. The effect of regular reflection, which depends upon the polish of surfaces, is not to make those surfaces visible, but to exhibit images of surrounding objects; it is by the light irregularly reflected upon their surfaces that objects are seen. In looking into a mirror, the image of the face is seen by regular reflection; the surface of the mirror is recognized by irregular reflection. "The mirrors of the ancients were of metal, usually of the compound now known as speculum-metal. Looking-glasses date from the twelfth century. They are plates of glass, coated at the back with an amalgam of quicksilver and tin, which forms the reflecting surface. This arrangement has the great advantage of excluding the air, and thus preventing oxidation. It is attended, however, with the disadvantage that the surface of the glass and the surface of the amalgam form two mirrors; and the superposition of the two sets of images produces a confusion which would be intolerable in delicate optical arrangements. The mirrors, or specula as they are called, of reflecting telescopes, are usually made of speculum-metal, which is a

Fig. 3.

Reflection by Water.

bronze composed of about thirty-two parts of copper to fifteen of tin. Lead, antimony, and arsenic, are sometimes added. Of late years specula of glass coated in front with real silver have been extensively used; they are known as silvered specula. A coating of platinum has also been tried, but not with much success."

It is well known that the effect of plane mirrors or of any polished plane surface is to produce behind them images exactly similar both in form and size to the real objects in front of them. Fig. 2 represents the formation of an image of a candle in a common looking-glass. The reflection is shown as limited to the pencil of rays emitted by the highest point of the flame. The reflected rays which enter the eye are seen to be divergent like the incident rays, so that if they were produced backward they would meet at a point forming the image at the top of the flame. As all surfaces are made up of points, and each point of the object is reflected in the same manner, it is clear that the image formed by a plane mirror must symmetrically represent the object.

Fig 4. Fig 5.
Appearance of a Stick in Water. Snell's Law of Refraction.

But light-rays may be turned from their direct course in another way. When a beam passes obliquely from one transparent medium to another of different density, as from air to water or glass, its direction is changed and it is said to be refracted. This is illustrated in a very simple manner by Fig. 3, in which a ray of the sun, entering through an aperture in a dark room and received on the surface of water in a glass vessel, is seen to be broken as it were at the surface and bent downward.

A familiar experiment illustrating the same principle is to put a coin upon the bottom of an empty, opaque vessel, while the spectator places himself so that it is just hidden by the vessel's edge. If water be now poured into it, the bottom of the dish will appear to rise, and the coin will come in sight. The pencil of rays thus undergoes a sudden bend at the surface of the water, and reaches the eye by a crooked course, the effect of which is, that the spectator sees round or behind the obstacle. Fig. 4 shows how an inclined stick, partially immersed in water, presents a broken appearance. Transparent substances differ in this refracting power. Liquids exhibit it in a much higher degree than gases, and, as a general rule, the denser of two substances manifests the greater refracting effect. Hence it is common to speak of the change in the ray as it passes from a denser into a rarer medium, or the reverse.

Although a ray when passing from one medium to another is refracted at different angles depending upon its obliquity, yet the phenomenon is governed by one law and capable of being expressed in one formula. This is called the index of refraction, and was discovered by Willebrod Snell, a Dutch philosopher, about the year 1621. Fig. 5 will illustrate it. A circle is described around the point I, at which the ray R is incident upon the refracting surface. As the angle of the incident ray R varies with the normal, the angle of the refracted ray S will vary also. The law of refraction is, that the signs of these angles as R' P', S P will have a constant ratio. Each transparent substance has its index of refraction, and tables are given of these indices for different substances in the books upon physics.

Fig. 6.

Theory of Mirage.

In order that a ray may be refracted, it is by no means necessary that it should pass through bodies of widely different qualities, as from gases to liquids, or from liquids to solids; the effect may be seen in passing from one liquid to another of a different density, as where liquid bisulphide of carbon is covered with a layer of water floating upon its surface. The ray will then be seen to be bent on entering the water, and still more bent on passing from the water into the layer of bisulphide of carbon. In the same way rays of light passing through layers of the atmosphere of different density, undergo successive refractions. As the atmosphere varies in its density as we ascend from the earth, the rays of the sun and stars in passing through them are bent in their course, so that in point of fact we see them all through crooked and varying paths.

An appearance, as of water, is often seen in sandy deserts, where the soil is highly heated by the sun. The observer sees in the distance the reflection of the sky and of terrestrial objects, as on the surface of a lake. Fig. 6 illustrates how this effect may be produced. The air near the ground becomes so highly heated and rarefied that its

Fig. 6.

Mirage of the Desert.

density within a certain distance increases upward. A ray, M A, Fig. 6, proceeding obliquely downward, will be rendered by refraction more and more nearly horizontal, until it is at length totally reflected, and it is then by successive refractions gradually elevated till it meets the eye of the observer at O, who thus sees an inverted image at M. Fig. 7 shows this effect as seen in the desert, where the eye is cheated by the appearance of water.

When a ray of light enters a piece of glass having parallel sides, as shown in Fig. 8, it is refracted, at the upper surface, downward, as in the case of water, and passes on straight until it reaches the lower surface. But, as it emerges, the reverse effect takes place, and the ray is refracted away from the perpendicular line. Its direction is now parallel to its original course, but it takes the path S instead of S' . The effect of this is, that whenever we look obliquely through plates of glass, as window-panes, all objects seen are slightly displaced, the degree of displacement varying of course with the thickness of the plate.

Fig. 8. Fig. 9.
Vision through Glass Plate. Refraction through Prism.

If, now, we take a piece of glass, of a wedge-shape, in which the sides are not parallel, a different effect is produced by the passage of the light through it. Such a piece of glass, or any transparent substance bounded by surfaces in this way, is called a prism. In Fig. 9, the ray S is represented as striking the prism at I, and, as it enters the glass, it is refracted toward the thicker part, and emerges at E. As it passes out into the air it is again bent in the same direction toward the base of the prism. The dotted lines, N I and E N' are drawn perpendicular to the faces of the prism, or at right angles, and serve to show that the path of the ray through the prism also makes equal angles with its surfaces.

The lines at which the faces of a prism meet are called its edge. Those in use are generally triangular, and very frequently equilateral, as shown in Fig. 10. For experiment, when used separately, they are commonly mounted upon stands, as shown in Fig. 11, which has several joints. The uppermost is for rotating the prism about its own horizontal axis; the second is for tilting it at an angle with the horizon; the third is for turning it about a vertical axis; and the fourth for raising and lowering it through a range of several inches.

When a prism like that shown in Fig. 9 is interposed in the path of a narrow beam of sunlight, admitted into a dark room, its alteration

Fig. 10. Fig. 11.
Equilateral Prism. Prism mounted on Stand.

of the direction of the ray is easily seen, and it will be found that the course of the light is altered, by refraction, some 40° or 50° from its original course.

The properties of light, to which we have here briefly referred, are interesting in themselves, and important to be known; but they have additional interest as preparing for an understanding of spectrum analysis, which will be taken up and popularly explained in future numbers of the Monthly.