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Optics}Total Internal Reflections

Total internal reflection is when one has a beam of light having all of the incident wave reflected. Going through a bit of formalism in electromagnetism one can derive Snell's Law for Total Internal Reflection,

where n_{inside}=1.33, and one assumes that the surface has n_{outside}=1 for air.

One must solve the equation \theta = \sin^{-1}(1/1.33). One can immediately throw out choices (A) and (E). From the unit circle, one recalls that \sin(30^{\deg})=1/2 and \sin(60^{\deg})=1.7/2=0.85. Since 1/1.33 \approx 0.7, one deduces that the angle must be choice (C).


See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
tensorwhat
2009-04-03 07:42:49
Easier way to think about this using critical angles for total internal reflection......

For a piece of plastic or glass with n=1.5 you have a critical angle of 41.5^o (look it up), so by decreasing the index of refraction (eg. water 1.33) you would slightly increase the critical angle so there about 50^o
ramparts
2009-11-03 18:06:23
Yeah. I'll be sure to look that one up on the test. Thanks a lot.
Alternate Solution - Unverified
Comments
torturedbabycow
2010-03-27 19:54:37
As far as solving that annoying inverse sine, I think the easiest way by far is to just draw out the triangle - one side is 1, and the hypotenuse is 1.33. So, since 1.33 is pretty close to \sqrt{2}, the angle should be pretty close to 45 degrees. Stare at the triangle a few more seconds, and it becomes obvious (at least to me) that it should be a little more than 45, so voila, answer (C)!NEC
jmason86
2009-10-01 19:33:10
This is probably one to just have memorized. Stupid ETS trying to make us solve that inverse sign of 1/1.33. I hate 'em.NEC
f4hy
2009-04-03 17:32:47
I only got this one because I remembered doing this exact problem in an optics class and knew that for water the angle is 50 degreesNEC
tensorwhat
2009-04-03 07:42:49
Easier way to think about this using critical angles for total internal reflection......

For a piece of plastic or glass with n=1.5 you have a critical angle of 41.5^o (look it up), so by decreasing the index of refraction (eg. water 1.33) you would slightly increase the critical angle so there about 50^o
ramparts
2009-11-03 18:06:23
Yeah. I'll be sure to look that one up on the test. Thanks a lot.
Alternate Solution - Unverified

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