Proof of total internal reflection
I have to prove that when a ray in the air (n=1) is penetrating in a long solid where n=1.5, there will always be a total internal reflection no matter what the orientation of the ray incident is.
First, I believe by "orientation" they mean the angle, correct me if it could be something else.
I tried to check what happens when I set the ray incident angle to 0 degrees and 90 degrees. (extreme values, so theoretically everything in between works too)
For:
(LaTeX doesn't seem to work at the moment)
1*sin 90 = 1.5*sin A
I have A = 41.81 degrees
and for:
1*sin 0 = 1.5*sin A
I have A = 0 degrees
Now I want to find the critical angle inside the solid that tells me if a ray will do a total internal reflection or not:
1.5 * sin B = 1 * sin 90
I have B = 41.81 degrees (of course since it is the same equation as the first)
So since my refracted angle is always inbetween 0 and 41.81 degrees, we can say that it will always be a total internal reflection.
This is my "solution" but I believe it is flawed (I have serious doubts about the method I used to find the critical angle)
Any help would be appreciated!
Thanks a lot in advance.
