What should be the maximum acceptance angle a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The acceptance angle $	heta_a$ is defined as the maximum angle that a light ray can make with the axis of the optical fibre and still be guided t

Vedclass · Accepted Answer

$\sin^{-1}\sqrt{n_1^2 - n_2^2}$

Vedclass · Answer

(B) The acceptance angle $	heta_a$ is defined as the maximum angle that a light ray can make with the axis of the optical fibre and still be guided through the core by total internal reflection.Applying Snell's Law at the air-core interface: $1 \cdot \sin 	heta_a = n_1 \cdot \sin 	heta_r$,where $	heta_r$ is the angle of refraction.At the core-cladding interface,for total internal reflection to occur,the angle of incidence $	heta_i$ must be at least the critical angle $	heta_c$,where $\sin 	heta_c = n_2/n_1$.Since $	heta_r + 	heta_i = 90^\circ$,we have $\sin 	heta_r = \cos 	heta_i = \sqrt{1 - \sin^2 	heta_i} = \sqrt{1 - (n_2/n_1)^2} = \frac{\sqrt{n_1^2 - n_2^2}}{n_1}$.Substituting this into the first equation: $\sin 	heta_a = n_1 \cdot \frac{\sqrt{n_1^2 - n_2^2}}{n_1} = \sqrt{n_1^2 - n_2^2}$.Therefore,$	heta_a = \sin^{-1}\sqrt{n_1^2 - n_2^2}$.

What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding,respectively?

Similar Questions

The speed of light in two media $c_1$ and $c_2$ are $1.5 \times 10^8 \ m/s$ and $2 \times 10^8 \ m/s$ respectively. If the light undergoes total internal reflection,the critical angle between the two media is

Explain the use of optical fibre in the medical field.

$A$ beam of light consisting of red,green and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the above red,green and blue wavelengths are $1.39, 1.44$ and $1.47$ respectively.
The prism will

$A$ ray of light travels from a denser medium $(\mu)$ to air. The angle of incidence is denoted by $i$ and the angle of deviation by $D$. Let $C = \sin^{-1}(1/\mu)$. Which of the following graphs is correct?

$A$ point source of light is placed at a depth $h = 0.5 \, m$ below the surface of a liquid $(\mu = \frac{5}{4})$. Then,the fraction of light energy that escapes directly from the liquid surface is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module