Question

When a beam of light of wavelength $\lambda$ is incident on the surface of a liquid at an angle $\theta$, the reflected ray is completely polarized. The wavelength of light in the liquid medium is

• A. $\lambda \tan \theta$
• B. $\frac{\lambda }{\tan \theta }$
• C. $\frac{\lambda }{\cos \theta }$
• D. $\frac{\lambda }{\sin \theta }$

Answer 1

The correct option is B $\frac{\lambda }{\tan \theta }$

Given:
Polarizing angle, $i_p=\theta$

According to Brewster's law
$\mu =\tan i_p$

$\therefore \mu =\tan \theta$

Also, when a light of wavelength $\lambda$ travels from air to a medium of refractive index $\mu$, the wavelength of light in medium,

${\lambda }_{medium}=\frac{\lambda }{\mu }=\frac{\lambda }{\tan \theta }$

Hence, option $\left(\text{B}\right)$ is correct.