Solution:
Given,
Critical angle (C) = 45°,
Polarizing angle (θp) =?
We know that,
\(\mu=\tan\left(\theta_p\right)\)
Or, \(\tan\left(\theta_p\right)=\mu=\frac1{\sin\left(C\right)}\)
Or, \(\theta_p=\tan^{-1}\left(\frac1{\sin\left(C\right)}\right)\)
Or, \(\theta_p=\tan^{-1}\left(\frac1{\sin\left(45^\circ\right)}\right)\)
Or, \(\theta_p=\tan^{-1}\left(\frac1{\displaystyle\frac1{\sqrt2}}\right)\)
Or, \(\theta_p=\tan^{-1}\left(\sqrt2\right)\)
∴ \(\theta_p=54.7^\circ\)
Hence, the required polarizing angle is 54.7°