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

Answer 1

Answer: (A)

We know that,
$\mu=\frac{\sin i}{\sin r} $ (Snell’s law)
and $i+r=90^{\circ}$
or $r=90^{\circ}-i$
$\Rightarrow \mu=\frac{\sin i}{\sin \left(90^{\circ}-i\right)}=\tan i$
or $i=\tan ^{-1}(\mu)=\tan ^{-1}(1.62)$