# Why does light refract?

I had read that light does slow down in glass because photons interact with atoms in glass. They are absorbed and re-emitted and during this phenomenon it's speed decreases. See also this and this Phys.SE post and links therein.

But then why does it bend? It has confused me a lot! Furthermore i have very little knowledge of Optics or Physics as a whole.

• The title doesn't correspond to the content of the question. The answer to the question posed in the title is that it's simply a matter of symmetry. – user4552 Jul 6 '13 at 0:47

A good question, and one that confused me for a long time.

In the absense of matter the light wave is massless. However in the presence of polarisable matter the light interacts with the matter and forms a composite system. Now you have a single wavefunction that describes the combined system and you can no longer separate it into a light bit and matter bit. This composite system propagates with a velocity of less than $c$.

The composite system of light and matter is called a polariton although I think strictly speaking the term polariton is reserved for strongly interacting systems such as Bose-Einstein condensates, where the speed of light can be reduced to only a few metres per second.

• Um... Except for the speed being less than c, I think most of this is wrong. – user93146 Jul 11 '18 at 16:23

Fermat's "Least Action Principle"

To understand the reason why this happens, you need to think in terms of Fermat's least action principle. The reason why light refracts is because it "optimises" its path. In other words, light takes the path of minimal time. This is the principle that was stated by Fermat, and if you do the mathematical analysis of it, which is not hard, you can derive Snell's law. In quantum mechanics this is explained by the infinitely many paths light takes, and the way in which the phasors add up to give the most probable path.

When light falls vertically on the interface of two media, the straight through path is the shortest path from time point of view. So there is no need for light to divert its direction. Of course, some of it will be reflected back out. For example if it is air-to-glass, I think about 4% will be reflected and the rest will be transmitted.

As for the question "why light slows down", it has been discussed elsewhere in this forum.

• This is true but it doesn't answer the question. Fermat's Least action principle is a mathematical model that express how light behaves when propagate classically but it does not give answer to why the light bends when refracting. If you think carefully, this is a very difficult question to answer since it involves the inner nature of light which is still as enigmatic as quantum mechanics itself. Further lecture – E.phy Mar 6 '18 at 2:53

A good motivational book to start to understand this is Feynman's "QED"

https://www.amazon.com/QED-Strange-Princeton-Science-Library/dp/0691164096/

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.

https://van.physics.illinois.edu/qa/listing.php?id=2223

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.

http://www.physicsclassroom.com/class/refrn/Lesson-1/The-Cause-of-Refraction

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.