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 = 47.6o with respect to the horizontal and enters the prism at a height h = 11 cm above the base. The beam leaves the prism to the air at a distance d = 27.6 cm along the base as shown.
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 n1*sin(θ1)=n2*sin(θ2)
The Attempt at a Solution
Okay, so I started by trying to find the angle (for angle two) for which all the light would be reflected. To find this, I know that the refracted angle will be 90°. Therefore, i think to find this angle it would just be sin^-1(n1/n2). (I used n1 to refer to the air=1, and n2 for the prism which i solved for earlier and got 1.5725). I believe if i take the complement of this angle i would get φ2. I don't really know how to go from here, or even if i did the above correctly.
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