A prism with refracting angle `60^@` gives angle of minimum deviation, `53^@, 51^@ and 52^@` for blue, yellow and red light respectively. What is the dispersive power of the prism ?

Explanation

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

### Step 1: Understand the given data
We have the following information:
- Refracting angle of the prism (A) = 60°
- Angle of minimum deviation for blue light (D_b) = 53°
- Angle of minimum deviation for yellow light (D_y) = 51°
- Angle of minimum deviation for red light (D_r) = 52°

### Step 2: Calculate the dispersive power
The formula for dispersive power (ω) of a prism is given by:

\[ \omega = \frac{D_v - D_r}{D_y} \]

where:
- \(D_v\) is the angle of minimum deviation for violet light (we will assume it is similar to blue for this calculation, as it is not provided),
- \(D_r\) is the angle of minimum deviation for red light,
- \(D_y\) is the angle of minimum deviation for yellow light.

In this case, we will assume \(D_v\) to be equal to \(D_b\) (53°) for the calculation.

### Step 3: Substitute the values
Substituting the values we have:

\[ \omega = \frac{D_b - D_r}{D_y} = \frac{53° - 52°}{51°} \]

### Step 4: Perform the calculation
Now, calculate the numerator and denominator:

Numerator:
\[ 53° - 52° = 1° \]

Denominator:
\[ 51° \]

Now, substituting these values into the formula:

\[ \omega = \frac{1°}{51°} \]

### Step 5: Final result
Thus, the dispersive power of the prism is:

\[ \omega = \frac{1}{51} \]