Refraction and Lenses Legacy Problem #7 Guided Solution

In this problem, I'm given a diagram in which it shows a ray of light passing from material A into material B, bending away from the normal line as it does. And I'm given that the index of refraction of material A is 2.24. That's the end value of material A. It says use your protractor to measure the angles and determine the index of refraction of material B. I wish to find the end value of B. I can use a protractor and just line it up on the diagram in order to measure the angle that the light ray makes with the normal line within material A and within material B. When I do that, I find it makes a 15 degree angle of incidence within material A. That's the angle between the incident ray and the imaginary normal line drawn to the surface. And in B, the angle ends up being 30 degrees. I'm using 15 degrees and 30 degrees even though I might have measured 16 and 32. I'm using 15 and 30 because it tells me that the angle measures are intended to be multiples of 15 degrees. Now I know three quantities about this refraction problem. I know the n1 value, n of material A, and the theta1 value, the angle of incidence within material A. And I know the theta2 value, the index of the angle of refraction within material B. And I want to find the fourth quantity, n2, or the index of refraction of material B. So to do that, I just substitute into the Snell's Law equation n1 sine theta1 equals n2 sine theta2. And it becomes 2.24 times the sine of 15 degrees is equal to nr, the unknown quantity, or n2, the unknown quantity, times the sine of 30 degrees. I can divide each side of the equation by the sine of 30 degrees to get n2 by itself. And then I can solve for n2, and I get 1.1595. And I can round that to the third significant digit.