A good motivational book to start to understand this is Feynman's "QED"
There are models of light that have been used. Consider the particle model. In this case you have a ball rolling along. It hits the top of a ramp and rolls down. And you find the ratio of speeds at top and bottom. And you are very amused to find it obeys Snell's law. But the problem is, it seems to have light going faster on the side where the index of refraction is higher. Hmm...
Then you get to use ripple tanks in your physics lab. And you measure the speed waves move as a function of depth.
Deeper water has faster waves. And you do the lab to get the speed at different depths in your ripple tank.
Then you build a model of a refracting surface. It's just a little platform so that you can have two depths in the tank at the same time.
Then you introduce waves that hit the edge of the platform at an angle. And you measure their angle on the other side. And you are amused that it obeys Snell's law. But now the waves are moving more slowly on the side that indicates higher index of refraction. And you think, Ahah! Light is waves.
Then your teacher gives you the killer assignment. Explain why waves change angle when they move from a faster to a lower speed region.
And you are looking at the row of marching people thinking, isn't that a particle theory again? But in the case of water, the answer is "kind of."
Water waves are motion of water particles. Each particle moves in a round-about up-and-down and back-and-forth motion and finishes not very far from where it started. Each particle is just doing what it does, and transmits some push to its neighbors. When you get to the edge, the push has to transmit to neighbors who are trying to move differently over the platform. So you get a difference in the net force transmitted. If you measured the platform you would find some net pushing on it.
Light is doing something like that, but it's photons instead of waves in water. Here you will need to read some more, such as Feynman's book.