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

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
  1. lies between $\sqrt{2}$ and 1
  2. lies between 2 and $\sqrt{2}$
  3. is less than 1
  4. is greater than 2

Solution

$\begin{aligned} \mu & =\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin A / 2} \\ & =\frac{\sin \left(\frac{A+A}{2}\right)}{\sin A / 2} \end{aligned}$ In given situation value of $A$ varies from 0 to $90^{\circ}$. So, $\mu_{\min }=2 \cos \frac{90^{\circ}}{2}=\sqrt{2}$ and $\mu_{\max }=2 \cos 0^{\circ}=2$

Asked in: NEET 2012 (Mains)

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