Question

The minimum deviation produced by a hollow prism filled with a certain liquid is found to be 30\(^\circ\). The light ray is also found to be refracted at an angle of 30\(^\circ\). Then the refractive index of the liquid is

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

Hint:

In refractive index calculations for hollow prisms, use the formula \( \mu = \sin\left( \frac{A + \delta}{2} \right) \), where \( A \) is the prism angle and \( \delta \) is the minimum deviation.

Answer 1

The Correct Option is A

For a hollow prism filled with a liquid, the refractive index \( \mu \) of the liquid is related to the minimum deviation \( \delta \) and the angle of the prism \( A \) by the formula: \[ \mu = \sin\left( \frac{A + \delta}{2} \right) \] Given that the minimum deviation \( \delta = 30^\circ \), we have: \[ \mu = \sin\left( \frac{30^\circ + 30^\circ}{2} \right) = \sin(30^\circ) = \frac{1}{2} \] Thus, the refractive index \( \mu \) is \( \sqrt{2} \).