For the angle of minimum deviation of a prism to be equal to its...

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

Options

Alies between $\sqrt{2}$ and 1
Blies between 2 and $\sqrt{2}$
Cis less than 1
Dis greater than 2

Correct answer

B. lies between 2 and $\sqrt{2}$

Step-by-step solution

\begin{aligned} \mu& =\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin A / 2}\\ & =\frac{\sin \left(\frac{A+A}{2}\right)}{\sin A / 2} \end{aligned}

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

\\ In given situation value of

varies from 0 to

90^{{}^{\circ}}

. So, \mu_{\min }=2 \cos

\frac{90^{{}^{\circ}}}{2}=\sqrt{2}

and

\mu_{\max }=2 \cos 0^{{}^{\circ}}=2$

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