00:01
Okay, so we're given the index of refraction on the left side, which is water, so it's 1 .33, given the angle of instance and the angle of refraction, and we're going to use that to find the index of refraction on inside the gemstone.
00:19
So we'll start with snell's law, which tells us n .i.
00:24
Sine theta i equals nf sign theta f and we can use that to find nf which is n i sine theta i over sine theta f and that tells us nf equals 1 .33 if we plug all this in times sine of 80 degrees over the sign of 15 .2 degrees.
01:16
And if we plug all that into our calculator, we find that nf equals 5 .0.
01:24
And now we can use this equation, v equals c over an f, to find the speed of light inside the gemstone.
01:34
So we plug in our values given to us, which is the speed of light 3 .0 times 10 to the 8 meters per second, and nf, which we just solved for, 5 .0.
01:49
And we find that the speed of light inside the gemstone is 6 .0 times 10 to the 7th meters per second.
02:08
And so that's the answer to part a.
02:12
And then part b asked us, what's unreasonable about this? and as we'll learn more later on in relativity, the speed of light should be the same in all frames of reference...