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  • For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose

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For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

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\mu\:=\:\frac{sin (\frac{A+\delta m}{2})}{sin(\frac{A}{2})}

Here \delta _{m}\:=\:A\:\:\:\:\:\:\:\:\therefore\mu\:=\:\frac{sin(\frac{A+A}{2})}{sin(\frac{A}{2})}=\frac{2sin\frac{A}{2}cos\frac{A}{2}}{sin\frac{A}{2}}

\mu=2cos\frac{A}{2}\ \, \, ------(1)

In the given situation A can varies from 0 to 90.

\therefore\:\mu_{mim}=2.cos(\frac{90}{2})=\sqrt{2}

\mu_{max}=2.cos0^{\circ}=2

\therefore\:\mu lies between \sqrt{2} and 2.

 

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Safeer PP

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