Question

Derive an expression for the acceptance angle and numerical aperture
of an optical fiber with core and cladding refractive indices being ni
and 12. Assume that it has been placed in a medium with refractive
index no​

Answer 1

Answer:

Definition: Numerical Aperture is the measure of the ability of an optical fiber to collect or confine the incident light ray inside it. It is among the most basic property of optical fiber.

derivation of Aperture of Optical Fiber

Consider a light ray XA, that incident inside the optical fiber. The refractive index of the core is ƞ1 and that of cladding is ƞ2.

The figure below shows an optical fiber inside which light ray is focused.

propagation through optical fiber

So, the ray XA is launched from denser medium to rarer medium by making an angle α with the fiber axis. This angle α is known as the acceptance angle of the fiber.

This incident ray propagates inside the fiber and gets reflected completely by the core-cladding interface.

But for this, the angle of the incident should be more as compared to the critical angle. Otherwise, if the incident angle is less the critical angle then rather being reflected, the ray gets refracted

According to Snell’s law, the incident and refracted ray propagate in the same plane. Hence, on applying Snell’s law at medium 1 (usually air) and core interface.