Question

Determine the maximum angle θ for which the light rays incident on the end of the light pipe in the figure below are subject to total internal reflection along the walls of the pipe. Assume that the pipe has an index of refraction of 1.33 and that the outside medium is air.
°?

Answer 1

Given that refractive index of pipe n_p = 1.33
The critical angle  θ_c = sin^-1 ( n_air /n_p)
                                 = sin^-1 ( 1.00 / 1.33)
                                 = 48.7
the refracted angle of the light beam is

                  θ_r = 90 - 48.7

                       = 41.2

     the incident angle is

                θ_i =sin^-1(n_psinθ_r /n_air )
                    = sin^-1 ( 1.33 sin (41.2) / 1.00)

                     = 61.1 degrees