How does total internal reflection relate to the formation of mirages?

Total internal reflection plays a key role in the formation of mirages, especially in hot environments like deserts or roads on sunny days.

Here’s how it works:

1. Temperature gradient in air:
   On a hot day, the ground becomes very warm and heats the layer of air just above it. This creates a temperature gradient—hot air near the surface and cooler air above.
2. Refractive index changes:
   Warm air is less dense and has a lower refractive index than cooler air. As light travels from cooler to warmer air, it bends away from the normal.
3. Gradual bending into total internal reflection:
   If the temperature gradient is steep enough, light rays from the sky bend more and more as they move downward. At a certain angle, instead of passing into the hotter air, the light undergoes total internal reflection and curves back upward.
4. Illusion of water:
   Our brain assumes light travels in a straight line. So when light from the sky is bent and reflected upward, we perceive it as coming from the ground. This creates the illusion of a puddle or water reflecting the sky.