Why Is the Angle of Incidence Crucial in Understanding Light Refraction?

[peter.ell]

I am a very conceptual kind of person and I'm trying to understand refraction, but after all my reading I'm still having some fundamental gaps that are preventing me from fully grasping it.

(All of these questions are especially pertaining to how light waves refract.)

Here's what I don't get:

1.) Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media. But what does it really mean to say that the sines of the angles of incidence are equivalent rather than the angles themselves as in the law of reflection?

2.) What is so important about the angle that a wave makes with the normal? If refraction is physically due to the wave's speed being slowed and it's wavelength shifting accordingly, then why is the degree of bending so dependent on the angle it makes with the normal? A light wave striking a piece of glass perpendicular to its surface, for example, will not be bent, it will go straight through, while a light wave striking that same piece of glass at an angle will not pass right through but will be bent first. What physically explains this, other than Snell's Law which just states it?

3.) Is there any physical explanation as to what causes a wave to bend toward or away from the normal depending on how its speed is changing?

Thank you so much for the help!

 

[JeffKoch]

Snell's law can be derived in various ways, you might start with that - the Wiki article on the topic has some useful graphs and animation, but it's more instructive to derive it and then refine any questions. Note that reflection and refraction are not different.

 

[Dr_Morbius]

If you think of the wave front as being like a line then as the bottom of the wave front hits the refracting material it begins to slow down while the top is still moving at its original velocity this causes the wave front to seem to rotate down towards the refracting surface.

http://en.wikipedia.org/wiki/Refraction

 

[sophiecentaur]

The wavelength in each medium is proportional to the speed. At the interface, the peaks of waves on each side must coincide as the wave passes through (a necessary boundary condition). This means that the angle must change to accommodate these two requirements. The geometry leads to Snell's Law. This is a bit of book-work that makes sense and is pretty understandable by anyone who can handle simple geometry.