6. Propagation of light in nonhomogeneous media - explanation of mirages. (4p.)

Question 1

Propagation of light in nonhomogeneous media

Answer 1

In a nonhomogenous medium, the velocity of propagation of light waves varies from point to point, so that we must describe the optical properties of the medium by giving the index of refraction as a function of position:

𝑛 = 𝑛 ( 𝑥 , 𝑦 , 𝑧 )

Question 2

Explanation of mirages.

Answer 2

Let’s consider a situation, where the refractive index varies continuously only in the z direction, but the wave can propagate freely in the y – z plane. Physically, this can occur in the atmosphere near the surface of the earth. The sun heats the earth, which heats the air just above the surface. Thus, over some region, the index of refraction of the air increases with height. Consequently light rays are curved upwards near the ground surface. Under these conditions, light from an object some distance above the ground surface may reach the eye of an observer either along a more or less straight path or along a curved path, which passes near this heated surface.

Thus, the observer will see the object approximately in its correct position, and, in addition, will see an inverted image of the object as if it were reflected by a water surface. This phenomenon, known as mirage, is commonly seen in the desert, creating the illusion of a body of water.