The refractive indices of crown glass for violet and red colours are respectively 1.523 and 1.513. Determine the dispersive power of this glass. If a crown glass prism produces a mean deviation of `40^(@)`, what will be the angular dispersion ?

Answer

To solve the problem, we need to determine the dispersive power of crown glass and the angular dispersion produced by a prism made of this glass. Let's break this down step by step.

### Step 1: Calculate the Dispersive Power of Crown Glass

The dispersive power (ω) of a material is given by the formula:

\[ \omega = \frac{\mu_v - \mu_r}{\mu - 1} \]

where:
- \(\mu_v\) = refractive index for violet light = 1.523
- \(\mu_r\) = refractive index for red light = 1.513
- \(\mu\) = mean refractive index

First, we need to calculate the mean refractive index (\(\mu\)):

\[ \mu = \frac{\mu_v + \mu_r}{2} = \frac{1.523 + 1.513}{2} = \frac{3.036}{2} = 1.518 \]

Now, we can substitute the values into the dispersive power formula:

\[ \omega = \frac{1.523 - 1.513}{1.518 - 1} = \frac{0.010}{0.518} \approx 0.0193 \]

### Step 2: Calculate the Angular Dispersion

The angular dispersion (Δ) produced by a prism can be calculated using the formula:

\[ \Delta = \omega \cdot D \]

where \(D\) is the mean deviation. Given that the mean deviation is \(40^\circ\):

\[ \Delta = 0.0193 \cdot 40^\circ \approx 0.772^\circ \]

### Final Results

1. The dispersive power of crown glass is approximately **0.0193**.
2. The angular dispersion produced by the prism is approximately **0.772°**.