00:01
So we're looking for the smallest possible incidence angle so that light that enters a prism with a refraction index of 1 .603 experiences total internal reflection.
00:14
And do that.
00:15
We're going to use snow's law here, which just says that the refraction index times the sign of the incoming angle is equal to the refraction index of the material that the light beam enters.
00:30
Times the sign of the refracted angle.
00:35
And we're going to make use of this and then some geometry of the problem.
00:41
And then we'll have to do some back substitution to eventually work our way to find theta 1.
00:47
But starting from step 1, we have n1, which is air, and that's 1 times the sign of theta 1, 1 .603 times a sign of theta 2.
01:06
And i'll label that equation 1.
01:11
And we can solve this for theta 1 and get the arc sine 1.
01:24
Let me do the .603 times a sine of theta 2.
01:34
And we'll come back to that.
01:39
But now we move on to equation two, which if you look at my diagram here, i have the light coming in at theta 1.
01:51
It's refracted at an angle theta 2 right here.
01:56
And then it hits the hypotenuse of the triangle where it goes perfectly down the hypotenuse.
02:03
And that is how you model internal reflection.
02:07
And to do that, it has to be parallel or rather perpendicular to the normal.
02:13
And what that means in terms of a math equation is we get the n, the glass times a sine of theta 3, which is this angle right here, equals the refractive index of the air, times the sine of 90 degrees, which equals 1.
02:38
We have 1 .603 times sine of theta 3 equals 1.
02:48
We can solve this for theta 3 and get the arc sign of 1 .603, which is 38 .59 degrees...