Snell's Law?

Question

Snell's Law is :

index of refraction = sin i / sin R

I know this much. So I plotted two graphs. The first graph is the angle of incidence vs the angle of refraction. The result is a curved line of best fit. The second graph is sine angle of incidence vs sine angle of refraction. The result is a straight line through the origin.

My questions are:

1. Why did the first graph have a curve line?

2. Why did the second graph, which are sine of the angles, have a straight line?

3. What does the slope in the graph represent?

Thank you in advance! ! !

Answer 1

Let's try question #2 first.

We can rewrite your formula by setting y = sin i and x = sin R, so we get y = (index of refraction) * x .

So, if you plot sin i vs. sin R, you get a straight line that goes through the origin (recall that for a line, y=mx+b where m is the slope and b is the y-intercept). So now we know that the slope of the line (m)  is just the index of refraction (and b=0).

If you plot the angles w/o the sines, you'll get curves unless you plot very small angles, since the graph of sin(x) is curvy (not a nice line). Hope this helps answer #1...