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 $\mu =\frac{1}{\sin {\theta }_c}\dots$(ii)
From Eqs. (i) and (ii), we get
$\frac{1}{\sin {\theta }_c}=\tan {\theta }_p$
or $\tan {\theta }_p\sin {\theta }_c=1$