Numerical Aperture and Angle of Acceptance of an optical Fiber. An optical fiber is illuminated by light from a source (e.g., a light-emitting diode, LED). The refractive indexes of the core and cladding of the fiber are n_1 and n_2, respectively, and the refractive index of air is 1 (Fig. 1.2- 18). Show that the half-angle theta_a of the cone of rays accepted by the fiber (transmitted through the fiber without undergoing refraction at the cladding) is given by (1.2-15) Numerical Aperture Optical Fiber The angle theta_a is called the acceptance angle and the parameter NA sin theta_a is known as the numerical aperture of the fiber. Calculate the numerical aperture and acceptance angle for a silica-glass fiber with n_1 1.475 and n_2 1.460. Figure 1.2-18 Acceptance angle of an optical fiber.