Question

Question: (a) At what angle of incidence will the light reflected from water be completely polarized? (b) Does this angle depend on the wavelength of the light?

Short answer

1. The incidence angle for the completely polarized reflected light for water is${\mathrm{\theta }}_{\mathrm{B}}=53.1^{\circ }$
2. The angle of incidence also depends on the wavelength of light.

Step-by-step solution

Given

Light reflected from the water is completely polarized.

 Step 2: Understanding the concept

By using the concept of Brewster’s angle, we can find the angle of incidence and whether it depends on the wavelength.

(a) Calculate at what angle of incidence will the light reflected from water be completely polarized

Suppose that the light is traveling from the air to the water.

So,${\mathrm{n}}_1=$the refractive index of air$=1$and${\mathrm{n}}_2=$the refractive index of water $=1.33$

A reflected wave will be fully polarized, if the incident, unpolarized wave strikes a boundary at Brewster's angle.

Brewster angle is given by

$\begin{array}{l}{\mathrm{\theta }}_{\mathrm{B}}={\tan }^{-1}\left(\frac{{\mathrm{n}}_2}{{\mathrm{n}}_1}\right)\\ {\mathrm{\theta }}_{\mathrm{B}}={\tan }^{-1}\left(\frac{1.33}{1}\right)\\ {\mathrm{\theta }}_{\mathrm{B}}=53.1^{\circ }\end{array}$

 Step 4: (b) Find out if the angle depends on the wavelength of the light

As${\mathrm{\theta }}_{\mathrm{B}}=\left(\frac{{\mathrm{n}}_2}{{\mathrm{n}}_1}\right)$

Since $\frac{{\mathrm{n}}_2}{{\mathrm{n}}_1}$depends on the wavelength of light, we can say that the angle of incidence also depends on the wavelength of light.