The angle of minimum deviation measured with a prism is `30^(@)` and the angle of prism is `60^(@)`. The refractive index of prism material is

Options

A. `sqrt2`
B. 1.5
C. `4/3`
D. `5/4`

Explanation

To find the refractive index of the prism material given the angle of minimum deviation (Δm) and the angle of the prism (A), we can use the formula:

\[ \mu = \frac{\sin\left(\frac{A + \Delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Angle of minimum deviation, Δm = 30°
- Angle of prism, A = 60°

2. **Calculate A + Δm**:
\[ A + \Delta_m = 60° + 30° = 90° \]

3. **Calculate \(\frac{A + Δm}{2}\)**:
\[ \frac{A + \Delta_m}{2} = \frac{90°}{2} = 45° \]

4. **Calculate \(\frac{A}{2}\)**:
\[ \frac{A}{2} = \frac{60°}{2} = 30° \]

5. **Substitute into the Refractive Index Formula**:
\[ \mu = \frac{\sin(45°)}{\sin(30°)} \]

6. **Find the Values of Sine**:
- \(\sin(45°) = \frac{1}{\sqrt{2}}\)
- \(\sin(30°) = \frac{1}{2}\)

7. **Substitute the Sine Values**:
\[ \mu = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \frac{1}{\sqrt{2}} \times 2 = \frac{2}{\sqrt{2}} \]

8. **Simplify the Expression**:
\[ \mu = \frac{2}{\sqrt{2}} = \sqrt{2} \]

9. **Final Answer**:
The refractive index of the prism material is \(\mu = \sqrt{2}\).