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Two parallel mirrors are separated by some distance and the medium between the two mirrors is...

Two parallel mirrors are separated by some distance and the medium between the two mirrors is not a vacuum or air. The distance between the mirrors is 0.2 meters. A light ray (EM wave) is incident on the first mirror at an angle of 26 degrees with respect to the normal. The ray bounces back and forth 45 times before it exits the mirror (A bounce is a trip from one mirror to the other mirror. Not bouncing two bounces back to the first mirror.) If it takes the light ray 13 x 10-8 s to exit the mirror. Then, this medium between the mirrors is placed on the interface of a flat surface. If light originates from this medium and travels into a vacuum, what is the angle needed for total internal reflection in degrees?

Assume it leaves the mirror exactly on the last bounce.

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