Question

Light from a denser medium 1 passes to a rarer medium 2. When the angle of incidence is $\theta$, the partially reflected and refracted rays are mutually perpendicular. The critical angle will be

• A. $si{n}^{-1}\left(cot\theta \right)$
• B. $si{n}^{-1}\left(tan\theta \right)$
• C. $si{n}^{-1}\left(cos\theta \right)$
• D. $si{n}^{-1}\left(sec\theta \right)$

Answer 1

The correct option is B $si{n}^{-1}\left(tan\theta \right)$


${\mu }_{1}sin\theta ={\mu }_2\times sin({90}^{\circ }-\theta )$
$\Rightarrow \frac{{\mu }_2}{{\mu }_1}=tan\theta$
For ${\theta }_c\Rightarrow {\mu }_1\times sin{\theta }_C={\mu }_2\times sin\left({90}^{\circ }\right)$
$sin{\theta }_C=\frac{{\mu }_2}{{\mu }_1}=tan\theta$
$\Rightarrow {\theta }_C=si{n}^{-1}\left(tan\theta \right)$

Why this question? Importance in JEE: Simple questions on direct application of important results- Snell's Law in this case- are asked in JEE Mains. This one is not to be missed.