A beam of light both reflects and refracts at the surface between air and glass. The index of refraction of the glass is 1.4. If the refracted and the reflected rays are perpendicular to each other, then the angle of incidence in the air is

• Correct answer
  A

  $\tan ^{-1}(1.4)$
• B

  $\sin ^{-1}\left(\frac{1}{1.4}\right)$
• C

  $\tan ^{-1}\left(\frac{1}{1.4}\right)$
• D

  $\sin ^{-1}\left(\frac{1.4}{\pi}\right)$

Solution

We have $\mathrm{i}+90^{\circ}+\mathrm{r}=180^{\circ}$ $\begin{aligned} & \Rightarrow \quad \mathrm{i}+\mathrm{r}=90^{\circ} \\ & \Rightarrow \mathrm{r}=90-\mathrm{i}\end{aligned}$ By Snell's law $1 \sin i=(1.4) \sin r$ $\Rightarrow 1 \sin i=1.4 \sin (90-i)$ $\Rightarrow \sin \mathrm{i}=1.4 \cos \mathrm{i} \Rightarrow \tan \mathrm{i}=1.4 \Rightarrow \mathrm{i}=\tan ^{-1}(1.4)$

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