Question

The angle of incidence at which, reflected ray is totally polarised for reflection from air to glass (refractive index $=n$) is:

• A. ${\sin }^{-1}n$
• B. ${\sin }^{-1}\frac{1}{n}$
• C. ${\tan }^{-1}\frac{1}{n}$
• D. ${\tan }^{-1}n$

Answer 1

The correct option is D ${\tan }^{-1}n$

The condition for this to work is that the refelected ray and refracted ray should perpendicular to each other i.e.,${\theta }_t=90-{\theta }_i$

${\eta }_{air}\sin {\theta }_i={\eta }_{glass}\sin {\theta }_t$
$\sin {\theta }_i={\eta }_{glass}\cos {\theta }_i$

$\Rightarrow {\eta }_{glass}=\tan {\theta }_i$
$\Rightarrow {\theta }_i={\tan }^{-1}{\eta }_{glass}={\tan }^{-1}n$