Answer Happy

A glass optical fiber "captures" a ray of light by imposing total internal reflection upon that ray, many times over. Once inside the glass, such a ray will undergo total internal reflection if it strikes the boundary between glass and air at an angle of incidence that is greater than the critical angle. Suppose that an optical fiber is flat on one end, with the end surface at right angles to the fiber's long axis, as shown. The index of refraction is n=1.4000 A ray of light is directed toward the center of the flat surface at the end of this fiber, at an incidence angle 8, with respect to the normal, as shown. The ray refracts toward the central axis of the fiber (here a dashed line) as it enters the glass. It then reaches the outer edge of the fiber. What is the greatest value (in degrees) for 8, that will allow total internal reflection to occur at the outer edge?