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A light ray is incident normally to the long face (the hypotenuse) of a 45°–45°–90° prism surrounded by air, as shown in the figure below. Calculate the minimum index of refraction of the prism for which the ray will totally internally reflect at each of the two sides making the right angle.

A horizontal ray is normally incident on the long, hypotenuse face of a right-triangular prism. The ray extends unbent to the upper leg of the triangular prism, then reflects to move straight down. The ray is then incident on the lower leg of the triangular prism, and reflects to the left. The ray finally passes unbent through the hypotenuse of the triangular prism and extends to the left.

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