Question

The step index fibre has relative refractive index of $0.88\%$. What is the critical angle at the core-cladding interface?

• A. ${84}^{\circ }{24}^{\prime }$
• B. ${81}^{\circ }{20}^{\prime }$
• C. ${80}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (A)

${84}^{\circ }{24}^{\prime }$

$\begin{array}{cc}& \text{relative refractive index}=\frac{n_1-n_2}{n_1}=0.88\%=\frac{0.88}{100}-\left(1\right)\\ n_1=\text{refractive index of fibre}& \\ n_2=\text{refractive index of surroundings}& \end{array}$

$\begin{array}{c}{Q}_c={\sin }^{-1}\left(\mu \right)\text{[for critical angle] where}u=\frac{n_2}{n_1}\\ \therefore \text{by(1)}\frac{n_1-n_2}{n_1}=\frac{0.88}{100}\\ \Rightarrow 1-\frac{n_2}{n_1}=0.88\times {10}^{-2}\Rightarrow 1-\mu =0.0088\\ \therefore \mu =0.9912\end{array}$

$\begin{array}{c}\therefore Q_c={\sin }^{-1}\left(0.9912\right)\\ \text{i.e}{Q}_c={84}^{\circ }24\text{)}\end{array}$

Hence option (A) is correct