Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 88

For preventing interference of waves in neighboring fibers and for mechanical protection, individual optical fibers are usually cladded by a material of a lower refractive index, as shown in Fig., where n 2 n 1.
a) Express the maximum angle of incidence a in terms of n 0 , n 1 , and n 2 for meridional rays incident on the core's end face to be trapped inside the core by total internal reflection. ( Meridional rays are those that pass through the fiber axis. The angle a is called the acceptance angle , and sin a the numerical aperture (N.A) of the fiber.)
b) Find a and N.A. if n 1 = 2, n 2 = 1.74, and n 0 = 1.