Optical fibers are used to transmit light over long distances, using the concept of total internal reflection. In this problem, we will learn the basic principle using a simplified model of an optical fiber. In the diagram below, the 'core' of the fiber, through which light can be transported from one end to the other, has a diameter of d = 100 micrometer and a refractive index of nf = 1.5. The core is surrounded by a 'cladding', with a slightly smaller refractive index of nc = 1.45. The optical fiber (core + cladding) is surrounded by air, with a refractive index of na 1. The length of the fiber is L = 50 meters. A point source of light is placed very close (at a distance < radius of the core) to the tip and on the central axis of the optical fiber, as shown. The source is flashed (on and off) momentarily (almost zero duration) at time t = 0, and a pulse of light was radiated uniformly in all directions. Total optical power emitted in this pulse of light is P.

a) Sketch the approximate trajectory of a light ray, which is emitted from the source at an angle of theta= 45 degrees.

b) Sketch the approximate trajectory of a light ray, which is emitted from the source at an angle of theta = 20 degrees.

c) Approximately how much power, P' will go through the core to the other end of the fiber? Ignore any absorption in the fiber.

d) Would all the light (of power P') reach the other end of the fiber at the same time (remember the light source was flashed on for an infinitesimal duration, i.e., all the light started together from the left end of the fiber)? Give a quantitative answer. The speed of light is 3 x 10^8 meters/sec.