A plane polarized blue light ray is incident on a prism such that...

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $δ = 60^{o}$ (see Figure- $1$ ). The angle of minimum deviation for red light from the same prism is $δ_{\min} = 30^{o}$ (see Figure- $2$ ). The refractive index of the prism material for blue light is $\sqrt{3}$ . Which of the following statement(s) is(are) correct?

The blue light is polarized in the plane of incidence

The angle of the prism is

45^{o}

The refractive index of the material of the prism for red light is

\sqrt{2}

The angle of refraction for blue light in air at the exit plane of the prism is

60^{o}

Solution:

For no reflection:

$\tan i = \sqrt{3}$

$\Rightarrow i = 60 °$

Applying Snell's law at left interface, we get

$\Rightarrow 1 \times \sin i = \sqrt{3} \times \sin r_{1} \Rightarrow \sin r_{1} = \frac{1}{2} \Rightarrow r_{1} = 30^{o}$

Now, for given values

$δ = i + e - A \Rightarrow 60 ° = 60 ° + e - A \Rightarrow e = A$

Then,

$A = r_{1} + r_{2} \Rightarrow r_{2} = A - r_{1} = 30^{o}$

For red light:

Expression to find minimum deviation is given by,

$μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})} = \frac{\sin (\frac{60 ° + 30 °}{2})}{\sin (\frac{60 °}{2})} = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \sqrt{2}$

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A plane polarized blue light ray is incident on a prism such that...

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A plane polarized blue light ray is incident on a prism such that...

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