By how much do the critical angles for red (660 nm) and violet (410 nm) light differ in a diamond surrounded by air?

Video Transcript

This is College Physics Answers with Shaun Dychko. We consider the critical angle for light that is inside diamond that is surrounded by air, we are gonna find the critical angle for different colors— first for red and then for violet—and then find the difference between them. So the formula for the critical angle is the inverse sin of the second medium divided by the first medium— the second medium is the air and the first medium is the diamond. So for red, we have to look up the index of refraction of of diamond for the color red and that's 2.410 from table [25.2]. So we have inverse sin of 1.000 divided by 2.410 and that's 24.5154 degrees and then the critical angle for violet in diamond is the inverse sin of 1.000 divided by 2.458 and this works out to 24.0062 degrees and so the difference in critical angles between these two colors is 0.509 degrees.