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## Homework Statement

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?

## Homework Equations

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.

https://www.smartphysics.com/Content/Media/Images/EM/25/h25_prism.png [Broken]

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