Problem in explanations about refracted light

Question

I'm trying to understand light's refraction properties but I find issue with every explanation I come across.

For instance, my book uses as an example a marching band which comes across a muddy terrain. Because they have to keep the same distance in each singular row, every row is going to rotate when it goes through the mud.

But, if instead every person didn't have to keep the same distance with the others on his row, when they crossed the mud they'd all just slow down, without deviating their path.

So, what's going on with light? Why should photons keep the same distance with one another in their "row", and as a consequence deviate when they change medium? Most certainly, it has something to do with light behaving as a wave, but I still don't understand it on an intuitive level.

Answer 1

Try thinking of different wavelengths as different strides. The longer strides you take, the less you get slowed down.

Answer 2

In the marching band model, the persons of a row are unaware of their neighbors in the row, so they cannot be required to keep a fixed distance to those neighbors. Instead, the persons of a row are collectively carrying a horizontal straight stick, representing the wavefront of that row, and each person aims to march perpendicular to the stick.

Answer 3

When light enters a media of different density at an angle, the part of the wave that hits the media first slows down while the part of the wave that is still in free air (or vacuum, as the case may be) is still travelling at its free-air velocity. This is what causes the light ray to bend or refract. Imagine trying to steer an automobile whose brakes are pulling on one side, or whose tires are in mud; the car will want to drift in the direction with greater resistance. (Okay, not a perfect analogy, but I think it works.)