Thermal MirageHeat Refraction / Optical Distortion

Thermal Mirage is never where you look. They are where the light came from.

On a hot day the road heats the thin layer of air lying on it, and hot air is less dense than the cooler air above. Light is slightly slower in air than in vacuum: the refractive index of air is about 1.0003, and that extra 0.0003 shrinks as the air thins. The second formula on this page says exactly this, using the ideal-gas law to turn temperature into density.

Now follow a ray of skylight heading down toward the road at a shallow angle. Each layer it enters is hotter and faster than the last, and Snell's law, the first formula, tips the ray a little further from the vertical at every step. If it starts shallow enough, it never reaches the road. It curves through a lowest point and climbs back up, into your eye. Your brain traces the ray back in a straight line to a spot on the road, and finds a piece of sky there. Bright, bluish, shimmering, flat: it reads as water.

The numbers are small. Between air at 15 °C and air at 50 °C, the refractive index changes by about three parts in a hundred thousand. That turns back only rays meeting the hot layer at less than about half a degree. This is why the puddle always lies far down the road and retreats as you drive toward it. The shimmer is turbulence: rising hot air keeps changing the bending.

Feynman explains this mirage in Chapter 26 of the first volume of his Lectures, using Fermat's principle: light takes the path of least time, and over a hot road the quickest route runs low.

Thermal Mirage never lies. They report the sky, from the wrong address.