A ray of light is incident at an angle $i$ on a glass slab of refractive index $\mu$. The angla between reflected and refracted light is $90^{\circ}$ Then, the relationship between $i$ and $\mu$ is

• A

  $i=\tan ^{-1}\left(\frac{1}{\mu}\right)$
• Correct answer
  B

  $\tan i=\mu$
• C

  $\sin i=\mu$
• D

  $\cos i=\mu$

Solution

As situation can be diagrammatically as below From law of reflection $$ i=\theta $$ Now, $\quad \theta+r+90^{\circ}=180^{\circ}$ $$ \begin{aligned} \Rightarrow \quad i+r+90^{\circ} &=180^{\circ} \\ r &=90^{\circ}-i \end{aligned} $$ Also, from Snell's law $\frac{\sin i}{\sin r}=\mu \Rightarrow \frac{\sin i}{\sin \left(90^{\circ}-i\right)}=\frac{\sin i}{\cos i}=\mu$ $\Rightarrow \tan i=\mu$

Hence, the correct answer is option: 'B'.