why the light Travels faster in hot air
Answers
Feynman was specifically referencing hotter and colder air, such as you would encounter above an asphalt road on a sunny day.
Light slows down in materials. This is mostly because they are Dielectric, meaning that the electromagnetic fields (i.e. light) passing through them turn the molecules into tiny dipoles, which then interfere with the original light, ultimately having the effect of slowing the light down.
This dielectric phenomenon has very little dependence on temperature. However, it does depend on the density of the air. If the air is more dense, there are more molecules around. That means the air becomes a stronger dielectric and slows light down more.
So light actually slows down more in dense air, not necessarily cold air. It just turns out that cold air is more dense. What air does is equalize the pressure in different places. If there's a pressure difference, that pushes the air around until the pressure difference is canceled out. But hot air can maintain the same pressure as cold air at lower density. This is because pressure is the effect of molecules bouncing at high speed. In hot air, the molecules are going faster, so we need less of them to create the same pressure.
Colder air up off the ground by a few feet has essentially the same pressure as hotter air lower down, but the colder air has higher density and slows light down more. Therefore, when light obeys Fermat's principle and takes the fastest possible path from point to point, if it starts and finishes in the cold air, it can still dip down into the hot air for a speed boost before coming back up. This effect is called refraction and accounts for mirages.
This is so as speed of light depends upon the density of the medium so hot air has it's molecules more denser so it travels faster.
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