What equation can be applied when investigating the causes of mirage of road?

Question

What equation can be applied when investigating the causes of mirage of road?

Answer 1

before you get to the equations, you want to know the factors involved in causing mirages on the road (and I am presuming the mirages form on a hot day)

as the sun heats the road, the road warms and heats the air above the road causing the air above the road to become warm; when the air becomes warm, its density decreases

now, consider light traveling through the air; light will go from point A to point B along the path of shortest time (not necessarily shortest distance)

keep in mind that the speed of light through air is faster when the air is of lower density, so light travels faster through less dense air

thus, if you are driving on a hot day and see a car in front of you, you might notice the license plate of the car appear to be on the road...this is because light will travel from the license plate to your eye along the fastest path...and on a hot day the fastest path is a curved path that goes from the back of the car in front of you, down near the road (where the air is hotter and the light speed greater) and then to your eyes...your brain interprets this to mean the license plate is in the road (since your brain assumes light always travels in straight lines)

so...the equations...you could talk about the equations dealing with the heating of the road...or equations describing how conduction and convection heat the air...or equations of refraction (Snell's Law) showing how light changes direction as the index of refraction of the medium changes..

this is a delightfully complicated issue, with lots of equations to choose from