Question

A ray of light falls on a transparent glass slab with refractive index (relative to air) of $\mathrm{1.62.}$ 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 $i={\tan }^{-1}(\mu )={\tan }^{-1}(1.62)$