Question

Minimum deviation for an equilateral prism is 30°, refractive index is:

• A. \( \sqrt{2} \)
• B. \( \sqrt{\dfrac{3}{2}} \)
• C. 2
• D. 4

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
An equilateral prism has an angle of prism \( A = 60^\circ \). The refractive index \( \mu \) of the material of the prism is related to the angle of minimum deviation \( \delta_m \) and the angle of the prism \( A \).
Step 2: Key Formula or Approach:
The prism formula is: \[ \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]
Step 3: Detailed Explanation:
1. Given: \( A = 60^\circ \) (equilateral) and \( \delta_m = 30^\circ \). 2. Substitute the values into the formula: \[ \mu = \frac{\sin\left(\frac{60^\circ + 30^\circ}{2}\right)}{\sin\left(\frac{60^\circ}{2}\right)} \] \[ \mu = \frac{\sin(45^\circ)}{\sin(30^\circ)} \] 3. Using trigonometric values \( \sin 45^\circ = \frac{1}{\sqrt{2}} \) and \( \sin 30^\circ = \frac{1}{2} \): \[ \mu = \frac{1/\sqrt{2}}{1/2} = \frac{2}{\sqrt{2}} = \sqrt{2} \]
Step 4: Final Answer:
The refractive index of the prism is \( \sqrt{2} \).