How does the car analogy explain refraction of light? Today, my Physics teacher explained the cause of refraction by using the car analogy
It goes like this :

Suppose a car is moving on a concrete road and obliquely enters some mud. Now, one of the front tires will enter the mud earlier than the other and it will slow down earlier. So, this tire will now travel a less distance in the time in which the tire which has still not entered the mud will travel a larger distance. Due to this, the car will rotate with the tire that entered the mud as its center and its direction will change.
I get this. But I'm a little confused about how we can relate this to light while assuming that it is a wave.
An explanation would be appreciated...
Thanks!
 A: Maybe this version of the same analogy is clearer for you. Instead of a car, we have a column of soldiers, say 4 soldiers wide, marching in perfect time. The column of soldiers is a better representations of the light wave than the 2 front wheels of the car, IMHO.
Now consider what happens when the column crosses the concrete / mud boundary at an oblique angle. The soldiers who step on the mud first will slow down earlier than the soldiers on the other side of the column, and the column will bend.
You don't even need a column of soldiers to achieve  this rotation effect. You can feel it for yourself by trying to walk along a boundary between a firm surface and sand, with one foot on the firm ground and the other on the sand. Your body will try to twist towards the sand. This gets very annoying within a couple of minutes. ;)
A: The Car analogy I was taught is that car is faster in concrete and slow in mud, so to travel from point A(in concrete) to point B(in mud) in the least amount of time, the car have to change the direction at the junction of the two roads. The explanation you gave doesn't have to follow the Fermat's principle, which is the fundamental principle in the phenomenon of refraction of light.
