Question

Determine the refractive index of an equilateral prism if the angle of minimum deviation is ${30}^0$.

• A. $\sqrt{3}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\sqrt{2}$

Answer 1

The correct option is D $\sqrt{2}$

It is to be remember that for a prism
$\mu =\frac{\sin \left(\frac{A+{\delta }_{min}}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
Here $\mu$ is refractive index of prism. A is angle of prism. ${\delta }_{min}$ is minimum angle of deviation.
And it is given that $A={60}^0{\delta }_{min}={30}^0$
Hence $\mu =\frac{\sin \left(\frac{{90}^0}{2}\right)}{\sin {30}^0}=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}$
$\mu =\sqrt{2}$