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  • A ray of light passing through a prism suffers minimum deviation. It is found that the angle of incidence is double the angle of re

A ray of light passing through a prism \left ( \mu =\sqrt{3} \right ) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ________ (in degrees)
 

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best_answer

For minimum deviation,

r_{1}=r_{2} \quad \text { and } \quad i=e

At {{\text { first }}} refraction \: \: site,

\begin{aligned} &\mu_{1} \sin i=\mu_{2} \sin r_{1} \\ &1 \times \sin i=\mu \sin \left(\frac{i}{2}\right) \end{aligned}

2 \sin \left(\frac{i}{2}\right) \cos \left(\frac{i}{2}\right)=(\sqrt{3}) \sin \left(\frac{i}{2}\right)

\begin{aligned} & \cos \left(\frac{i}{2}\right)=\frac{\sqrt{3}}{2} \\ \end{aligned}

\begin{aligned} \frac{i}{2} &=30^{\circ} \\ \end{aligned}

\begin{aligned} i &=60^{\circ} \\ \end{aligned}

\begin{aligned} \because A &=r_{1}+r_{2}=\frac{i}{2}+\frac{i}{2} \\ &=60^{\circ} \end{aligned}

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vishal kumar

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