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Wave Optics

Question

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Use the formula of refractive index of a prism to calculate the angle of minimum deviation for an equilateral triangular prism of refractive index √3.

Solution

Given,

Refractive index of prism, μ = \sqrt{3} A n g l e o f p r i s m, A = 60 °

Now using the prism formula,

μ = \frac{\sin (A + δ_{m}) / 2}{\sin A / 2}

\Rightarrow

\sqrt{3} = \frac{\sin \frac{δ_{m} + 60 °}{2}}{\sin 60 ° / 2}

\Rightarrow

\sqrt{3} \times \sin 30 ° = \sin (\frac{δ_{m} + 60 °}{2})

\Rightarrow

\sin (\frac{δ_{m} + 60 °}{2}) = \sqrt{3} \times \frac{1}{2} = \sin 60 °

\Rightarrow

\frac{δ_{m} + 60 °}{2} = 60 °

\Rightarrow

δ_{m} + 60 ° = 120 °

∴

δ_{m} = 60 °

is the required minimum angle of deviation.

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