The refractive index of the prism for violet colour is 1.7 and that for red is 1.65. Then dispersive power of the material of prism is

Options

A. 0.74
B. 0.074
C. 0.054
D. 0.015

Answer

To find the dispersive power of the material of a prism given the refractive indices for violet and red light, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Refractive index for violet light, \( \mu_V = 1.7 \)
- Refractive index for red light, \( \mu_R = 1.65 \)

2. **Calculate the Refractive Index for Yellow Light**:
- Since the refractive index for yellow light is not provided, we can estimate it using the average of the refractive indices for violet and red light:
\[ \mu_Y = \frac{\mu_V + \mu_R}{2} = \frac{1.7 + 1.65}{2} = \frac{3.35}{2} = 1.675 \]

3. **Use the Formula for Dispersive Power**:
- The formula for dispersive power \( \omega \) is given by:
\[ \omega = \frac{\mu_V - \mu_R}{\mu_Y - 1} \]

4. **Substitute the Values into the Formula**:
- Substitute \( \mu_V \), \( \mu_R \), and \( \mu_Y \) into the dispersive power formula:
\[ \omega = \frac{1.7 - 1.65}{1.675 - 1} \]

5. **Calculate the Numerator and Denominator**:
- Numerator:
\[ 1.7 - 1.65 = 0.05 \]
- Denominator:
\[ 1.675 - 1 = 0.675 \]

6. **Calculate the Dispersive Power**:
- Now, substitute the values into the equation:
\[ \omega = \frac{0.05}{0.675} \approx 0.074 \]

7. **Final Result**:
- The dispersive power of the material of the prism is approximately \( 0.074 \).