# Derivation of Law of Refraction

1. Sep 13, 2010

### FeDeX_LaTeX

Hello;

I have learned that the law of refraction is n = sinI/sinR, where n is the refractive index, I is the angle of incidence, and R is the angle of refraction.

But why is it sinI/sinR, and not simply angle I/angle R if it is identifying the ratio between the two angles?

I have heard that I need to do some trigonometric manipulation but I don't know what this manipulation is. Thanks.

(i.e. if I = 60 degrees, and R = 30 degrees, then the refractive index is sqrt(3), not 2... but why? how was this law derived?)

2. Sep 13, 2010

### zhermes

You can derive it from Fermat's principle (least time), or from hamilton's principle. The key is that it only depends on the component of velocity parallel to the surface.
There is also the old, 'running along the sand--swimming across the river' in the least time example which gives you the same result.

3. Sep 13, 2010

### Studiot

4. Sep 18, 2010

### FeDeX_LaTeX

Hello;

Apologies for the delay between replies; I have no internet access so I have to wander around the street looking for hotspots. Thanks for the link - it helped me formulate a way to geometrically show why Snell's Law is true. I also found this, which helped too: http://farside.ph.utexas.edu/teaching/316/lectures/node128.html