You are working in an optical research laboratory. One of the pieces of experimental apparatus involves a beam of light entering a transparent rod (see the figure below) of diameter d = 4.50 um and index of refraction n = 1.23, surrounded by air.

Your supervisor has given you the task of determining the cone of acceptance for the rod, which is the maximum angle θmax (in degrees) for which the light rays incident on the end of the rod are subject to total internal reflection along the walls of the rod.
One of the pieces of experimental apparatus involves a beam of light entering a transparent rod (see the figure below) of diameter d = 4.50 um and index of refraction n = 1.23
Assume a transparent rod of diameter d = 3.75 µm has an index of refraction of 1.34. Determine the maximum angle θ for which the light rays incident on the end of the rod in the figure below are subject to total internal reflection along the walls of the rod. Your answer defines the size of the cone of acceptance for the rod.