Question

A light ray entering an optical fiber (made from crown glass) surrounded by air is first refracted and then reflected as shown below 2 1 a. What is the minimum angle 01 (greater than or equal to 0) at which an incident ray will still be totally internally reflected? Hint for (a) Minimum angle 61 deg. (Only enter values 0 or greater.) b. What is the maximum angle 61 (smaller than 90 deg) at which an incident ray will still be totally internally reflected? Hint for (b) Maximum angle θ deg c. If the optical fiber is made with material other than crown glass, what minimum value n is needed for refractive index of the material to ensure that all incident rays are totally internally reflected? Hint for (c) Minimum n, needed

Answer 1

Given that A light ray entering an optical fiber surrounded by air a) minimum angle theta_1 = 0 degree why because in this case theta_2 will be zero and theta_3 will be 90 degree, so TIR will take place b) maximum angle theta_1 = 90 degree why because in this case theta_2 = sin^-1 (n_1/n_2) = sin^-1 (1/1.517) = 41.24 which is also critical angle for TIR theta_3 = 90-41.24 = 48.76 degree which is mole the critical angle 41.24 degree so TIR will take place c) In limiting case, toil maximum theta_1 if theta_2 is 45 degree, theta_3 will be 45 degree and her TIR will take place minimum n_2 = n_1/sin 45 degree = squareroot 2 = 1.414