The formation of a mirage

What is a mirage? How is it formed?

Fig. 1  In regions of air with temperature decreases with altitude, light will travel in a curved path due to refraction.

Fig. 2  Refraction occurs when a light beam travels from glass to the air. The angle of incidence i is smaller than the angle of refraction r.

Fig. 3  Total internal reflection occurs when the incident angle i is larger than the critical angle c.

Fig. 4   The path of light when a mirage happens.

A traveler has lost his way in the desert. Enduring thirst and hunger, he suddenly saw an oasis, so the overjoyed man quickly ran towards it. To his great disappointment, it was just an illusion produced by a mirage. Such an episode was often pictured in movies, yet the optical magic that the nature plays with us - mirage - really exists in reality. Its formation is a result of the refraction and the total internal reflection of light in the air.

To investigate the formation of a mirage, we firstly need to understand why light is refracted in the air. Regions of air at different temperatures have different refractive indexes, just like many different mediums. The closer the air is to the ground, the hotter it will be, and its refractive index will be smaller. We could imagine the air as many layers of medium with a particular refractive index for every layer, and the refractive index is smaller for those that are closer to the ground. Thus when light travels in air, its path is as shown in Fig.1.

On the other hand, we should also understand what total internal reflection is. If light travels from glass to the air with a small incident angle, part of the light will be reflected back while the remaining part will be refracted, passing out from the glass. As the refractive index of glass is larger than that of the air, the refracted angle is always larger than the incident angle (Fig. 2). When the incident angle becomes larger, the refracted light will get closer and closer to the interface between the air and the glass. When it is larger than the critical angle, the light will only be reflected but not refracted. This phenomenon is called total internal reflection (Fig. 3).

Fig. 4 shows the path of light when a mirage happens. Suppose there is an oasis and the light it emits at point A is refracted by the air, the light will travel through a curved path. Total internal reflection occurs at point B and will cause the light to travel upwards. Then the light is refracted by the air again. At last, it will enter the eyes of the observer at point C, producing an illusion that the oasis is close to him.

Total internal reflection has been discovered for a long time already. Some of its broad applications include optical fibre, single lens reflex camera and binocular telescope.