path by the density of the refracting medium. The angle formed by the refracted ray with the normal is called the angle of refraction.

d. The angle of refraction depends on the relative density of the two mediums, as well as on the angle of incidence. An equation, known as Snell's law, may be used to determine the angle of refraction (r) if the angle of incidence (i) and the index of refraction (par. 14 b) of each medium are known. This equation is:

sin i sin r

= n

where n is the quotient of the indices of refraction of the two mediums. If one of the mediums is air, n is the index of refraction of the second medium.

14. INDEX OF REFRACTION.

a. Light travels through substances of different densities with greatly varying velocities. For example, the speed of light in air is approximately 186,000 miles per second; in ordinary glass, it is approximately 120,000 miles per second.

b. The ratio between the speed of light in air and the speed of light in a second medium is known as the index of refraction. The index of refraction is usually indicated by the letter n and is determined by dividing the speed of light in a vacuum by the speed of light in the particular medium.

C. The following table contains the index of refraction of each of a number of substances pertaining to optics. NOTE: For most computations, the index of air is considered to be unity (1.000).

15. ATMOSPHERIC REFRACTION.

a. At a surface separating two media of different indices of refraction, the direction of the path of light changes abruptly when passing through the surface. If the index of refraction of a single medium changes gradually as the light proceeds from point to point, the path of the light will also change gradually and will be curved rather than in a straight line.

b. Although air at its densest has a refractive index of only 1.000292, this is sufficient to bend light rays from the sun toward the earth when these rays strike the atmosphere at an angle (fig. 26). The earth's atmosphere is a medium which becomes denser toward the surface of the earth. The result is that a ray of light traveling through the atmosphere toward the earth at an angle does not travel in a straight line but is refracted and follows a curved path. From points near the horizon, the bending of light is so great that the setting sun is seen after it is completely below the horizon (fig. 27).

C. The bending of the paths of rays of light in a horizontal plane is not due to any systematic variation of the refractive index. This

variation is generally so small that it can be neglected in many types of observation made with fire control instruments. In very careful surveys of large areas, this effect is eliminated by repeating the observations on different days and under different conditions. In the aiming of guns over wide expanses of water, as must be done by coast artillery, a special instrument, the depression position finder, takes atmospheric refraction as well as other conditions into consideration.

d. Over large areas of heated sand or over water, conditions are such as to produce strata or layers of air differing greatly in temperature and refractive index. Under such conditions, erect or inverted and sometimes much distorted images are formed which can be seen from a great distance. These images are known as mirages.

e. On a hot day, the columns of heated air rising from the earth are optically different from the surrounding air, and paths of light are irregularly reflected. The air is turbulent and conditions under which observations are made are changing all the time. Consequently, an object viewed through such layers of air appears to be in motion about a mean position. In such cases, the air is said to be "boiling" or the image is "dancing," due to "heat waves." This condition is particularly detrimental when a high-power telescope is employed. Under such conditions it is usually impossible to use an instrument of more than 20 power.

16.

REFRACTION THROUGH A TRIANGULAR GLASS PRISM. a. Refraction through a triangular glass prism differs from refraction through a sheet of glass with parallel surfaces because the light which penetrates the base or thicker part of the prism must travel longer and at less speed in a denser medium than the light passing through the apex or thinner part of the prism. Rays of light emerging from a plate of glass with parallel surfaces always travel in a parallel direction with the incident rays; rays emerging from a prism always travel at different angles from the incident rays.

b. The laws of refraction apply to prisms just as they do to plates of glass with parallel surfaces. These laws may be applied to plot the paths of light through any prism.

C. When a ray of light strikes the surface of a prism, the refracted ray (fig. 28) is bent toward the normal according to the law of refraction. The refracted ray is bent away from the normal on leaving the prism. Thus, the path of the ray is deviated at the first surface of the prism and then further deviated at the second surface. In both cases, the ray is bent toward the thickest part of the prism.

17. REFRACTION THROUGH LENSES.

a. Convergent Lens. If two prisms are arranged base to base (fig. 29), rays of light striking the front surfaces will pass through the prisms. The rays emerging from one prism will cross the emergent rays of the other prism.

b. If the two prisms are cut in semicircular form, their surfaces made spherical, and the two bases cemented together, the result will be an optical element known as a convergent lens. (All convergent lenses are thicker at the center than at the edges.) When rays of light strike the front surfaces of a convergent lens (fig. 30), all rays pass through the lens and converge to a single point where they cross (color and other aberrations are disregarded at this time). Such a lens may be thought of as consisting of an infinite number of prisms arranged so that each direct light rays to a single point. The lens bends the rays as a prism does, but, unlike a prism, it brings them to a point.

C. Myriads of rays may be considered to come from every point of light on an object. Consider the refraction of three such rays from a point of light passing through a convergent lens (fig. 31) to intersect at a point on the other side of the lens. On the basis

that a lens bends the rays as a prism does, rays passing through the upper and lower portions of the lens would be bent toward the thickest part of the lens upon striking the first surface, and bent again toward the thickest part in emerging. As the result, they would converge on the other side. A straight line drawn through the center of the two spherical surfaces is termed the axis of the lens. A central or axial ray would not be deviated because it would strike the surfaces of the lens at the normal. Such a ray would join the outer rays at their convergent point.

d. The laws of refraction may be applied to plot the path of any ray through any lens. A ray entering a lens will bend toward the normal of the lens at that point (fig. 32). The normal of an incident ray at any point on a lens in an imaginary line at right angles to the surface of the lens at the point where the ray enters. As the refracted ray leaves the lens as the emergent ray, it is bent away from its