The deviation caused for red, yellow and violet colours for crown glass prism are `2.84^(@),3.28^(@)` and `3.72^(@)` respectively. The dispersive power of prism material is:

Options

A. `(11)/(41)`
B. `(92)/(250)`
C. `(117)/(250)`
D. `(22)/(57)`

Explanation

To solve the problem of finding the dispersive power of the prism material based on the given deviations for red, yellow, and violet colors, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Deviation for red (\( \delta_r \)) = \( 2.84^\circ \)
- Deviation for yellow (\( \delta_y \)) = \( 3.28^\circ \)
- Deviation for violet (\( \delta_v \)) = \( 3.72^\circ \)

2. **Write the formula for dispersive power (\( \omega \)):**
The dispersive power of the prism material is given by the formula:
\[ \omega = \frac{\delta_v - \delta_r}{\delta_y} \]

3. **Substitute the values into the formula:**
\[ \omega = \frac{3.72^\circ - 2.84^\circ}{3.28^\circ} \]

4. **Calculate the numerator:**
\[ \delta_v - \delta_r = 3.72 - 2.84 = 0.88^\circ \]

5. **Now substitute the calculated numerator back into the formula:**
\[ \omega = \frac{0.88^\circ}{3.28^\circ} \]

6. **Perform the division:**
\[ \omega = 0.2677 \quad (\text{approximately}) \]

7. **Convert to a fraction (if necessary):**
To express this as a fraction, we can simplify:
\[ \omega = \frac{11}{41} \quad (\text{after simplifying the decimal}) \]

8. **Final answer:**
The dispersive power of the prism material is \( \frac{11}{41} \).