Question

A ray of light falls on a transparent glass slab with refractive index (relative to air) of $1.62$. The angle of incidence for which the reflected and refracted rays are mutually perpendicular is

• A. ${\tan }^{-1}\left(1.62\right)$
• B. ${\sin }^{-1}\left(1.62\right)$
• C. $\cos -1\left(1.62\right)$
• D. None of these

Answer 1

Answer: (A)

${\tan }^{-1}\left(1.62\right)$

From law of reflection:-

$r=i$

And from figure:-

$R+{90}^o+r={180}^o$

$⟹R={90}^o-r$

$⟹R={90}^o-i$

Now from Snell's Law:-

$\frac{\sin i}{\sin R}=\mu$

$⟹\frac{\sin i}{\sin ({90}^o-i)}=\mu$

$⟹\frac{\sin i}{\cos i}=\mu$

$⟹\tan i=\mu ⟹i={\tan }^{-1}\mu$

$i={\tan }^{-1}\left(1.62\right)$

Answer-(A)