Red light is incident in air on a 30o - 60o - 90 o prism as shown. The incident beam is directed at an angle of φ1 = 44o with respect to the horizontal and enters the prism at a height h = 16 cm above the base. The beam leaves the prism to the air at a distance d = 41.5 along the base as shown.
What is φ3, the angle the transmitted beam makes with the horizontal axis?
φ2 = 49.22 degrees
n2, index of refraction inside the prism = 1.47
Snell's Law: n1sinφ1 = n2sinφ2
The Attempt at a Solution
I dropped a normal line between φ2 and φ3, so that I could find the angle of incident as α = 90-φ2 = 40.78. Then I used Snell's Law to calculate the angle of refraction β = 73.76 degrees. This angle is complementary to φ3, so 90 - β =16.24. For some reason this isn't the answer, though everything I know tells me it should be.