Question

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

• A. ${60}^0$
• B. ${75}^0$
• C. ${45}^0$
• D. None of these

Answer 1

The correct option is D

None of these

Step 1: Given data.

Relative refractive index$=0.88\%$

Step 2: Finding the critical angle at the core-cladding interface.

We know that,

Relative refractive index$=\frac{{\mu }_1-{\mu }_2}{{\mu }_1}$

Where, ${\mu }_1$and ${\mu }_2$ are the refractive index of medium first and second respectively.

$0.88\%=\frac{{\mu }_1-{\mu }_2}{{\mu }_1}$

$\frac{0.88}{100}=\frac{{\mu }_1-{\mu }_2}{{\mu }_1}$

$100\left({\mu }_1-{\mu }_2\right)=0.88{\mu }_1$

$100{\mu }_1-0.88{\mu }_1=100{\mu }_2$

$\frac{{\mu }_2}{{\mu }_1}=\frac{100-0.88}{100}$

$\frac{{\mu }_2}{{\mu }_1}=0.9982$ ……..$\left(i\right)$

Now,

Critical angle, ${\theta }_c={\sin }^{-1}\left(\frac{{\mu }_2}{{\mu }_1}\right)$

${\theta }_c={\sin }^{-1}\left(0.9982\right)$ $\left[\because fromequation\left(i\right)\right]$

${\theta }_c={89}^{0}24\text{'}$

Hence, option D is correct.