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 = 37.6o with respect to the horizontal and enters the prism at a height h = 26 cm above the base. The beam leaves the prism to the air at a distance d = 73.1 cm.
What is φ1,max, the maximum value of φ1 for which the incident beam experiences total internal reflection at the horizontal face of the prism?
Snell's Law : n1sin(φ1) = n2sin(φ2)
geometric relations of a 30-60-90 triangle
The Attempt at a Solution
I used what I got for my n of the triangle, which is correct, at 1.289, and got a critical angle using the fact that for total internal reflection, the angle must be 90 so i got φ = sin^-1(1/1.289) which equals 50.877 degrees. My problem lies within the geometry of the situation, I've tried adding/subtracting all combinations of 90, 60, and 30. I can't seem to get what the φ1, max would be though.