A convex lens has mean focal length of 20 cm. The dispersive power of the material of the lens is 0.02. The longitudinal chromatic aberration for an object at infinity is

Options

A. `10^(3)`
B. 0.8
C. 0.4
D. 0.2

Explanation

To find the longitudinal chromatic aberration for a convex lens with a given mean focal length and dispersive power, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Longitudinal Chromatic Aberration (LCA)**:
- LCA is the difference in focal lengths for different wavelengths of light. It can be calculated using the formula:
\[ LCA = \omega \times f \]
where \( \omega \) is the dispersive power of the lens material, and \( f \) is the mean focal length of the lens.

2. **Identify Given Values**:
- Mean focal length, \( f = 20 \) cm
- Dispersive power, \( \omega = 0.02 \)

3. **Substitute the Values into the Formula**:
- Plug the values into the LCA formula:
\[ LCA = 0.02 \times 20 \text{ cm} \]

4. **Calculate the Longitudinal Chromatic Aberration**:
- Perform the multiplication:
\[ LCA = 0.40 \text{ cm} \]

5. **Final Answer**:
- The longitudinal chromatic aberration for the lens is \( 0.40 \) cm.

### Summary of the Calculation:
- \( LCA = \omega \times f = 0.02 \times 20 = 0.40 \) cm