Answer to Question #90083 in Optics for Shivam Nishad

Question

What is a step - index fibre ? Obtain an expression for the angle of incidence beyond which light will get refracted into the cladding material. What will happen if the refractive index of the cladding is higher than that of the core ?

Answer 1

A fiber with a uniform refractive index in its core that is a step below the refractive index of the cladding is called as step-index fibe.

We get using Snell’s law for the optical fiber

$$n_0 \sin i=n_1 \sin θ (1)$$

When the angle of incidence at core-cladding interface should be greater than θ'c then the light move in the core of optical fiber. As i increases, θ increases and so θ' decreases. Therefore, there is maximum value of angle of incidence beyond which, it does not propagate rather it is refracted in to cladding medium. This maximum value of i say i_m is called maximum angle of acceptance and n₀×sin i_m is termed as the numerical aperture (NA).

$$NA=n_1 \sin θ (2)$$

Using (1) we get:

$$NA=\sqrt {n_1^2- n_2^2}$$