Question

${\lambda }_a$ and ${\lambda }_m$ are the wavelengths of a beam of light in air and medium respectively. If $\theta$ is the polarising angle, the correct relation between ${\lambda }_a,{\lambda }_m$ and $\theta$ is:

• A. ${\lambda }_a={\lambda }_m{tan}^2\theta$
• B. ${\lambda }_m={\lambda }_a{tan}^2\theta$
• C. ${\lambda }_a={\lambda }_m\cot \theta$
• D. ${\lambda }_m={\lambda }_a\cot \theta$

Answer 1

The correct option is D ${\lambda }_m={\lambda }_a\cot \theta$

Polarizing angle is given by:

$tan\left(\theta \right){=}_1{\mu }_2$

$tan\left(\theta \right)=\frac{{\mu }_2}{{\mu }_1}...........\left(i\right)$

$\mu \propto \frac{1}{v}$

$v\propto \lambda$

$⟹\mu \propto \frac{1}{\lambda }.............\left(ii\right)$

From (i) and (ii),

${\lambda }_a={\lambda }_{m}tan\left(\theta \right)$

${\lambda }_m={\lambda }_{a}cot\left(\theta \right)$