the velocities of light in those media, a conclusion substantiated by the measurements of the velocity of light in water and in bisulphide of carbon by Foucault and Michelson.

We thus find that the wave theory leads to a simple and natural explanation of the facts known about refraction, a result which must strengthen our conviction of the essential soundness of the theory.

Also the index of refraction of a substance takes on a new interest when we think of its physical significance as the ratio of the velocity of light in air or vacuum to that in the substance.

840. Total Reflection.-When light passes from one medium into another in which the velocity of light is greater, as when

a/b/cd

it passes from water or glass into air, the refracted ray is bent away from the normal. Thus light in the direction Oa is refracted along the direction aa', that in the direction ob is refracted along bb', and finally a ray in the direction Od is refracted along dd', barely grazing the surface. A ray, such as Oe, which is more inclined than Od has no corresponding direction in the upper medium; it is therefore totally reflected at e as if it had fallen on a polished metal surface, and takes the direction ee'.

N

FIG. 502.

841. Critical Angle. The angle OdN beyond which refraction cannot take place is called the critical angle. From the law of refraction,

or the sine of the critical angle is equal to the reciprocal of the index of refraction.

842. Illustration of Total Reflection.-If a tumbler full of

water and having smooth sides is held in the hand, on looking down obliquely into it the sides are seen as polished, mirror-like surfaces reflecting objects under the glass but through which the fingers holding it cannot be seen if the surface is dry, as in that case light coming up from below is totally reflected at the surface. If the fingers are moist they will be seen

only at the spots where they press against the glass.

A right-angled glass prism having all its sides polished may be used as a mirror to turn a beam of light through 90° if the light falls upon it as shown in the figure, for in that case it meets the

oblique surface inside the glass at 45°, FIG. 503.-Total reflecting prism. which is greater than the critical angle

for glass and air. The intensity of the beam reflected in this way is far greater than if reflected from the outside of the same surface, for in that case a large amount of light is lost by refraction through the prism.

In figure 504 is shown a right-angled prism used as a reversing prism with a projecting lantern. The beam AA' which on entering the prism is directed downward, on leaving it is sloping upward, so also BB' is changed from an upward inclination on entering the prism to an equal downward slope on emergence.

843. Refraction of Gases.-The refracting power of gases is small compared with that of solids or liquids, the change in velocity when light passes from vacuum into air under ordinary

conditions being only about one

nine-hundredth

part of the change in velocity when it enters water. Yet

it is the variations of this small refractive power caused by the fluctuating density in the hot-air currents over a stove that cause the unsteadiness in the appearance of bodies seen through the stream of hot air.

844. Atmospheric Refraction.-In consequence of the refraction of the air the apparent angular distances of stars from the

zenith is less than their true zenith distances, the rays being refracted just as much as if the atmosphere terminated abruptly in a level surface just above the observing telescope and all above was vacuum, instead of gradually diminishing in density as it does. The sun or moon when seen near the horizon appears flattened in consequence of the lower edge being more raised by refraction than the upper edge, and when apparently just above the horizon it is really entirely below it.

845. Mirage. When a layer of air next the surface of the earth becomes heated it may become less dense and less refracting than the cooler layers above it, so that the lower edges of light

waves coming from a distant object are less retarded than the upper parts of the waves, and consequently the wave fronts swing around and come upward to the eye, as shown in figure 505. The distant object is thus seen inverted as if reflected in a horizontal mirror. In this way the familiar mirage of the desert may give the impression that objects seen are reflected in a sheet of water.

PRISMS AND LENSES.

846. Refraction of Plane Waves by Plate with Parallel Sides. In passing into the plate the beam is bent toward the normal, but since the two sides are parallel the waves within the plate make the same angle with one side as with the other and

will therefore be bent as much on emerging from the plate as they were bent on entering, and the emergent beam will therefore be parallel to the entering one, but displaced sidewise by an amount which depends on the thickness of the plate. Light waves from a distant point will therefore enter the eye of an observer in the same direction as

if the plate were not there.

If the apparent position of a star shifts on interposing a piece of thick plate glass, even if held obliquely, it is because the sides of the plate are not perfectly parallel.

847. Refraction by a Prism. -Plane waves when refracted at a plane surface remain plane, and therefore will continue plane after any number of successive refractions at plane surfaces.

FIG. 506.-Refraction through plate with parallel sides.

When a substance has two plane refracting surfaces which are inclined to each other it is called a prism, and the angle between the two refracting surfaces is called the angle of the prism.

A

E

In figure 507 the edge of the prism at A is supposed to be perpendicular to the plane of the paper, which is the plane of incidence. The beam of light at B enters the prism, is bent aside, and on emergence is again bent, and passes out in the direction shown at C. The total change in direction is represented by the angle CDE, which is called the deviation of the beam.

FIG. 507.-Refraction through a prism.

The beam is bent toward the thicker part of the prism, as shown in the figure, when the substance of the prism is more refracting than air, because that part of each wave is most retarded which is farthest from the edge of the prism and has to pass through the greatest thickness of retarding substance.

848. Minimum Deviation.-In such a position of the prism as that shown in figure 508, in which the incident beam makes the same angle with the first face of the prism as the emergent 'beam does with the second, it is found that the deviation angle CDE is a minimum; turning the prism away from this position in either direction causes the angle CDE to increase.

E

FIG. 508.-Minimum deviation.

If n represents the index of refraction of the substance of the prism, and if A is its angle and D the angle of minimum deviation, it may be easily proved that

849. Lenses.-Lenses are pieces of glass or other transparent substance usually bounded by spherical surfaces, and are used in forming optical images. The line joining the centers of