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 ray.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The difference between the angle of minimum deviation of violet (ΔV) and red (ΔR) rays is given as:
\[ ΔV - ΔR = 2^\circ \]
- The angle of minimum deviation for the mean ray (ΔY) is given as:
\[ ΔY = 48^\circ \]

2. **Identify the Mean Deviation:**
- The mean ray is typically considered to be the yellow ray in the context of the visible spectrum. Therefore, we can denote:
\[ ΔY = 48^\circ \]

3. **Use the Formula for Dispersive Power:**
- The formula for dispersive power (ω) of the material of the prism is given by:
\[ ω = \frac{ΔV - ΔR}{ΔY} \]
- Here, \(ΔV - ΔR\) is the angular dispersion, and \(ΔY\) is the mean deviation.

4. **Substitute the Values:**
- From the information provided:
\[ ΔV - ΔR = 2^\circ \]
\[ ΔY = 48^\circ \]
- Substitute these values into the formula:
\[ ω = \frac{2^\circ}{48^\circ} \]

5. **Calculate the Dispersive Power:**
- Perform the division:
\[ ω = \frac{2}{48} = \frac{1}{24} \]
- To express it in decimal form:
\[ ω \approx 0.04167 \]

6. **Conclusion:**
- The dispersive power of the material of the prism is approximately:
\[ ω \approx 0.0416 \]

### Final Answer:
The dispersive power of the material of the prism is \(0.0416\).