The angles of minimum deviations are 530 and 51° for blue and red colours respectively produced in an equilateral glass prism. The dispersive power is

Options

A. `51/26`
B. `1/26`
C. `1/52`
D. `1/51`

Explanation

To find the dispersive power of the prism, we can follow these steps:

### Step 1: Understand the given data
We are given the angles of minimum deviation for blue and red colors:
- Angle of minimum deviation for blue light (ΔB) = 53°
- Angle of minimum deviation for red light (ΔR) = 51°

### Step 2: Calculate the angle of minimum deviation for the mean color (yellow)
The mean color (yellow) can be approximated as the average of the angles of minimum deviation for blue and red:
\[ \Delta_{yellow} = \frac{\Delta_B + \Delta_R}{2} = \frac{53° + 51°}{2} = \frac{104°}{2} = 52° \]

### Step 3: Use the formula for dispersive power
The formula for dispersive power (ω) of the prism is given by:
\[ \omega = \frac{\Delta_B - \Delta_R}{\Delta_{yellow}} \]
Substituting the values we have:
\[ \omega = \frac{53° - 51°}{52°} = \frac{2°}{52°} = \frac{1}{26} \]

### Step 4: Conclusion
Thus, the dispersive power of the prism is:
\[ \omega = \frac{1}{26} \]