Chapter 33: Q 68P (page 1006)

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?

Expert verified

The incidence angle for the completely polarized reflected light for water is $θ_{B} = 53 . 1^{\circ}$
The angle of incidence also depends on the wavelength of light.

Step by step solution

Light reflected from the water is completely polarized.

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

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

So, $n_{1} =$ the refractive index of air $= 1$ and $n_{2} =$ 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

$\begin{array}{l} θ_{B} = \tan^{- 1} (\frac{n_{2}}{n_{1}}) \\ θ_{B} = \tan^{- 1} (\frac{1.33}{1}) \\ θ_{B} = 53 . 1^{\circ} \end{array}$

As $θ_{B} = (\frac{n_{2}}{n_{1}})$

Since $\frac{n_{2}}{n_{1}}$ depends on the wavelength of light, we can say that the angle of incidence also depends on the wavelength of light.

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