Question

If $\theta_p$ is the polarizing angle for a glass plate of refractive index $\mu$ and critical angle $\theta_c$, then

• A. $\theta_p=\theta_c$
• B. $\tan \theta_p \cdot \sin \theta_c=1$
• C. $\theta_p \theta_c=1$
• D. $\tan \theta_p=\sin \theta_c$
• E. $\tan \theta_p \sin \theta_c=\mu$

Answer 1

Answer: (B)

As we know, according to Brewster's law, refractive index,
$\mu=\tan \theta_p \text {.(i) }$
where, $\theta_p$ is polarising angle. Critical angle,
$\sin \theta_c=\frac{1}{\mu}$
Or $\mu=\frac{1}{\sin \theta_c} \ldots$(ii)
From Eqs. (i) and (ii), we get
$\frac{1}{\sin \theta_c}=\tan \theta_p$
or $\tan \theta_p \sin \theta_c=1$