How does a mirage form?

One of the most interesting effects of atmospheric refraction occurs in the mirage, which is usually associated with hot deserts. Mirage is the result of atmospheric refraction and total internal reflection.

The air in the desert is hot near the ground and cools rapidly with height. The hotter air is optically less dense. So as height increases the density of air increases, in this case.

mirage - refraction and total internal reflection
fig 1: mirage

Rays of light from the top of a tree (or the sky) suffer bending as they pass from one upper layer (which is cooler and denser) to its lower (relatively warmer and rarer) layer.

Thus rays of light pass layers of decreasing density, each time bending away from the normal to the point of incidence at the separating layers. This results in the gradual increase of the angle of incidence.

Eventually, a stage comes when the angle of incidence exceeds the critical angle and, therefore, total internal reflection takes place. After this, the rays start bending upwards. And this time as rays of light pass layers of increasing density they go on bending towards the normal line.

An observer sees the tree upside down (as well as the actual tree) as if he were seeing the reflection on a surface of the water (Fig. 1).

On hot summer days, motorists quite often see similar mirages on the roads.

How does a mirage form?
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