Question

A silicon optical fibre with a core diameter large enough has a core refractive index of $1.50$ and a cladding refractive index $1.47$. Determine:
(i) the critical angle at the core cladding interface
(ii) the numerical aperture for the fibre
(iii) the acceptance angle in air for the fibre.

Answer 1

Hint: Optical fibres are mainly used to transmit light. It is transmitted through the two ends of the fibre. Some of the characteristics of optical fibre include flexibility and transparency. Optical fibres are usually made of drawing glass or plastic. It has a diameter which is slightly thicker than the human hair.

Complete step by step answer:
(i) Critical angle $θ_c$ at the core-cladding interface is given by:
${\theta _c} = {\sin ^{ - 1}}\left( {\dfrac{n}{u}} \right)$
Here n is the refractive index of cladding and u is the refractive index of core material.
$\begin{array}{l}
{\theta _c} = {\sin ^{ - 1}}\left( {\dfrac{{1.47}}{{1.50}}} \right)\\
 = 78.5^\circ
\end{array}$

Thus, the critical angle is $78.5^\circ $.

(ii) Numerical aperture NA is given by:
$\begin{array}{l}
NA = \sqrt {\left( {{u^2} - {n^2}} \right)} \\
      = \sqrt {\left( {{{1.50}^2} - {{1.47}^2}} \right)} \\
      = 0.30
\end{array}$

Thus, the numerical aperture is 0.30.

(iii) Acceptance angle A is given by:
$\begin{array}{l}
A = {\sin ^{ - 1}}\;NA\\
   = {\sin ^{ - 1}}\;\left( {.30} \right)\\
   = 17.4^\circ
\end{array}$

Thus, the acceptance angle is $17.4^\circ $.

Additional Information: The optical fibres have a very low power loss compared to other cables in long distance transmission. It is not affected by electro-magnetic interference, which helps in reducing noise. The optical fibres have a comparatively low size which makes it more convenient. Optical fibres are lighter to carry. This makes it easy to port from one to another. They can transmit greater bandwidth than other cables. Since there is no electromagnetic energy emission it is really difficult to tap which makes it more secure

Note: Since it transmits light rather than electrons there will be no electromagnetic radiation. One of the disadvantages of optical fibres is that it is expensive to install. Due to its compactness and small size it is highly susceptible to getting damaged easily.