Light enters the flat circular end of an optical fiber at an angle of incidence of 60^ . The ray then hits the curved side wall exactly at the critical angle, resulting in grazing emergence into the surrounding air cladding. The refractive index of the fiber core is:

Step-by-step solution

Let the refractive index of the fiber core be and the angle of refraction at the flat end be r . Applying Snell's law at the flat entry surface: 1 60^ = r r = 3 2 Inside the fiber, the ray strikes the curved side wall. From the geometry of the cylinder, the normal to the side wall is perpendicular to the normal at the flat end. Thus, the angle of incidence at the side wall is 90^ - r . For grazing emergence into the air cladding, this angle must equal the critical angle c . (90^ - r) = c = 1 r = 1 Using the trigono