The refractive indices of crown and flint glasses for violet and red light are `1.523, 1.513, 1.773` and `1.743` respectively. Find the dispersive powers of the glasses.

Answer

To find the dispersive powers of crown and flint glasses, we will use the formula for dispersive power, which is given by:

\[ \text{Dispersive Power} = \frac{\mu_v - \mu_r}{\mu_{\text{mean}} - 1} \]

where:
- \(\mu_v\) is the refractive index for violet light,
- \(\mu_r\) is the refractive index for red light,
- \(\mu_{\text{mean}}\) is the average refractive index of the two colors.

### Step 1: Calculate the dispersive power for crown glass

1. **Identify the refractive indices for crown glass:**
- \(\mu_v = 1.523\) (for violet light)
- \(\mu_r = 1.513\) (for red light)

2. **Calculate \(\mu_{\text{mean}}\) for crown glass:**
\[ \mu_{\text{mean}} = \frac{\mu_v + \mu_r}{2} = \frac{1.523 + 1.513}{2} = \frac{3.036}{2} = 1.518 \]

3. **Substitute values into the dispersive power formula:**
\[ \text{Dispersive Power} = \frac{1.523 - 1.513}{1.518 - 1} = \frac{0.010}{0.518} \approx 0.0193 \]

### Step 2: Calculate the dispersive power for flint glass

1. **Identify the refractive indices for flint glass:**
- \(\mu_v = 1.773\) (for violet light)
- \(\mu_r = 1.743\) (for red light)

2. **Calculate \(\mu_{\text{mean}}\) for flint glass:**
\[ \mu_{\text{mean}} = \frac{\mu_v + \mu_r}{2} = \frac{1.773 + 1.743}{2} = \frac{3.516}{2} = 1.758 \]

3. **Substitute values into the dispersive power formula:**
\[ \text{Dispersive Power} = \frac{1.773 - 1.743}{1.758 - 1} = \frac{0.030}{0.758} \approx 0.0396 \]

### Final Results:
- Dispersive power of crown glass: **0.0193**
- Dispersive power of flint glass: **0.0396**