Refracting angle of a prism is 2 radians. Refractive indices of its material for violet and red are respectively 1.62 and 1.5 Dispersion produced by it is

Options

A. 0.24
B. 0.06
C. 1.66
D. 1.12

Explanation

To solve the problem of finding the dispersion produced by a prism with a given refracting angle and refractive indices for violet and red light, we can follow these steps:

### Step 1: Understand the given values
- Refracting angle of the prism (A) = 2 radians
- Refractive index for violet light (n_v) = 1.62
- Refractive index for red light (n_r) = 1.5

### Step 2: Write the formula for dispersion
The formula for dispersion (D) produced by a prism is given by:
\[ D = (n_v - n_r) \cdot A \]
where:
- \( n_v \) is the refractive index for violet light,
- \( n_r \) is the refractive index for red light,
- \( A \) is the refracting angle of the prism.

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ D = (1.62 - 1.5) \cdot 2 \]

### Step 4: Calculate the difference in refractive indices
First, we calculate the difference between the refractive indices:
\[ n_v - n_r = 1.62 - 1.5 = 0.12 \]

### Step 5: Multiply by the refracting angle
Next, we multiply the difference by the refracting angle:
\[ D = 0.12 \cdot 2 = 0.24 \]

### Step 6: State the final answer
Therefore, the dispersion produced by the prism is:
\[ D = 0.24 \]

### Conclusion
The correct answer is 0.24.

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