Answer to Question #162569 in Optics for Carty

Question

The critical angle for total internal reflection for sapphire surrounded by air is 34.4 degree. Calculate the polarizing angle for sapphire.

Answer 1

Answer

For critical angle for total internal reflection

$\frac{n_s}{n_a}=\frac{sin90^°}{sin\theta_c}$

Where s for sapphire and a for air

$n_s=\frac{1}{sin\theta_c}=\frac{1}{sin34.4^°}$

Now polarization angle

$\theta_p=\tan^{-1}(\frac{n_s}{n_a}) \\=\tan^{-1}(\frac{n_s}{1}) \\=\tan^{-1}(\frac{1}{sin34.4^°}) \\=60.5^°$