Physics - Why does a mirage happen in the desert?

Why does a mirage happen in the desert?

It is due to the phenomena of 'total internal reflection'. On a very hot day in a desert, the air just in contact with sand is hotter than the air above it due to the high temperature of sand. This causes the refractive index of the air in contact with the sand to be lower than that of the air above it. Thus, sunlight passes through a medium of higher refractive index to that of lower refractive index.

 At a particular angle, the angle of incidence becomes greater than the critical angle and all the conditions of total internal reflections are fulfilled. This causes the sunlight to reflect from the interface of both the air columns itself without touching the sand. Hence, it appears as a watery surface from far off distances, also known as mirage.

 While going nearer to the apparent water, the angle of incidence of sunlight decreases and becomes less than the critical angle. So, total internal reflection does not occur for that point at that angle and hence the mirage disappears.

Mirage is thus visible only when the distance from a point is greater than a critical distance determined by the refractive index of the air columns to satisfy the condition of critical angle for total internal reflection to occur.