The difference between angle of minimum deviation of violet and red rays in the spectrum of white light from a prism is `2^(@)`. If angle of minimum deviation of mean ray is `48^(@)`, the dispersive power of material of the prism is

Options

A. 48
B. 24
C. 0.032
D. 0.0416

Explanation

To solve the problem, we need to find the dispersive power of the material of the prism using the given information about the angles of minimum deviation for violet and red rays, as well as the mean angle of deviation.

### Step-by-Step Solution:

1. **Identify Given Values:**
- The difference between the angle of minimum deviation of violet and red rays (angular dispersion) = \(2^\circ\)
- The angle of minimum deviation of the mean ray (mean deviation) = \(48^\circ\)

2. **Understand the Formula for Dispersive Power:**
- The dispersive power (\(\omega\)) of a prism is given by the formula:
\[ \omega = \frac{\text{Angular Dispersion}}{\text{Mean Deviation}} \]

3. **Substitute the Values into the Formula:**
- Here, the angular dispersion is \(2^\circ\) and the mean deviation is \(48^\circ\).
- Plugging these values into the formula gives:
\[ \omega = \frac{2^\circ}{48^\circ} \]

4. **Calculate the Dispersive Power:**
- Performing the division:
\[ \omega = \frac{2}{48} = \frac{1}{24} \]
- Converting this to a decimal:
\[ \omega \approx 0.04167 \]

5. **Final Answer:**
- Therefore, the dispersive power of the material of the prism is approximately:
\[ \omega \approx 0.0416 \]