For a material medium, the values of refractive index for violet and colours are given as `n_(v) =1.56 and n_r=1.44`. The dispersive power of a prism made out of this material is

Options

A. 0.06
B. 0.24
C. 0.03
D. none of these

Answer

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

### Step 1: Understand the formula for dispersive power
The dispersive power (ω) of a prism is given by the formula:
\[ \omega = \frac{\text{Angular Dispersion}}{\text{Mean Deviation}} \]

### Step 2: Calculate Angular Dispersion
Angular dispersion is defined as the difference in refractive indices for violet (n_v) and red (n_r) light multiplied by the angle of the prism (A):
\[ \text{Angular Dispersion} = (n_v - n_r) \cdot A \]
Given:
- \( n_v = 1.56 \)
- \( n_r = 1.44 \)

Calculating the difference:
\[ n_v - n_r = 1.56 - 1.44 = 0.12 \]
Thus,
\[ \text{Angular Dispersion} = 0.12 \cdot A \]

### Step 3: Calculate Mean Deviation
Mean deviation is calculated using the mean refractive index (n_m) and the angle of the prism (A):
\[ \text{Mean Deviation} = (n_m - 1) \cdot A \]
The mean refractive index (n_m) can be calculated as:
\[ n_m = \frac{n_v + n_r}{2} = \frac{1.56 + 1.44}{2} = \frac{3.00}{2} = 1.50 \]
Now, substituting this into the mean deviation formula:
\[ \text{Mean Deviation} = (1.50 - 1) \cdot A = 0.50 \cdot A \]

### Step 4: Substitute into the Dispersive Power Formula
Now we can substitute the values we calculated into the dispersive power formula:
\[ \omega = \frac{0.12 \cdot A}{0.50 \cdot A} \]
The angle of the prism (A) cancels out:
\[ \omega = \frac{0.12}{0.50} = 0.24 \]

### Final Answer
Thus, the dispersive power of the prism made from this material is:
\[ \omega = 0.24 \]