Refraction of Light

the change in the direction of the propagation of light upon its passage through the interface between two mediums. At an unbounded plane interface between homogeneous, isotropic, nonabsorbing (transparent) mediums with the refractive indexes n₁ and n₂, the refraction of light is defined by two regularities. First, the refracted ray lies in the plane passing through the incident ray and the normal (perpendicular) to the interface surface; second, the angles of incidence Φ and of refraction x (see Figure 1) are related by Snell’s law, which states n₁ sin Φ = n₂ sin X.

Figure 1. The path of light rays upon refraction at a plane surface dividing two transparent mediums. The broken line represents the reflected ray. The angle of refraction is greater than the angle of incidence. This indicates that medium 1 is optically less dense than medium 2. Thus, n₁ < n₂. The normal to the surface of the interface is designated by n.

The refraction of light is accompanied by the reflection of light. In this case, the sum of the energies of the refracted and reflected pencils of light, whose quantitative expression follows from Fresnel’s equations, is equal to the energy of the incident pencil of rays. Their relative intensities depend on the angle of incidence, the values of n₁ and n₂, and the polarization of light in the incident pencil of rays. In the case of normal incidence, the ratio of the average energies of the refracted and the incident light waves is equal to 4n₁n₂/(n₁ + n₂)². In the important, particular case of light passing from air (n₁ = 1 to a high degree of accuracy) into glass with n₂ = 1.5, this quantity is 96 percent.

If n₂ < n₁ and if the angle of incidence Φ ≥ arc sin (n₂/n₁), refraction of light does not occur, and the entire energy of the incident light wave on the interface is transferred to the reflected wave (total reflection). At any value of Φ, with the exception of Φ = 0, the refraction of light is accompanied by a change in the state of polarization of the light; this change is strongest at the Brewster angle Φ = arc tan (n₁/n₂). The phenomenon is used in obtaining plane-polarized light. The dependence of the refraction of light on the polarization of incident rays is clearly seen in double refraction in optically anisotropic mediums.

The same equations are used in formal descriptions of the indexes of refraction of both absorbing and nonabsorbing mediums. In treating absorbing mediums, however, n is regarded as a complex quantity, the imaginary part of which characterizes the absorption of light by the medium. In this case, x also becomes complex and loses the meaning of a simple angle of refraction that it has for nonabsorbing mediums. In general, n of a medium depends on the wavelength of light X; for this reason, the component rays of nonmonochromatic light with various X travel along different paths when refracted (dispersion of light).

The laws governing the refraction of light form the basis for the configuration of lenses and many optical devices used to change the direction of light rays and to obtain optical images.