Relative difference of focal lengths of objective and eye lens in the microscope and telescope is given as

Options

A. It is equal in both
B. It is more in telescope
C. It is more in microscop
D. It may be more in any one

Answer

To find the relative difference of focal lengths of the objective and eye lens in a microscope and telescope, we will break down the problem step by step.

### Step-by-Step Solution:

1. **Define the Focal Lengths**:
- Let \( f_o^T \) be the focal length of the objective lens in the telescope.
- Let \( f_e^T \) be the focal length of the eye lens in the telescope.
- Let \( f_o^M \) be the focal length of the objective lens in the microscope.
- Let \( f_e^M \) be the focal length of the eye lens in the microscope.

2. **Determine the Differences**:
- For the telescope, the difference in focal lengths is given by:
\[ \Delta f^T = f_o^T - f_e^T \]
- For the microscope, the difference in focal lengths is given by:
\[ \Delta f^M = f_o^M - f_e^M \]

3. **Analyze the Focal Lengths**:
- In both cases (telescope and microscope), the focal length of the objective lens is greater than that of the eye lens:
\[ f_o^T > f_e^T \quad \text{and} \quad f_o^M > f_e^M \]
- Therefore, both differences \( \Delta f^T \) and \( \Delta f^M \) are positive.

4. **Compare the Focal Lengths**:
- The focal length of the objective lens in a telescope is generally larger than that in a microscope because telescopes are designed to view distant objects (like stars), requiring longer focal lengths.
- Thus, we can conclude:
\[ f_o^T > f_o^M \]

5. **Conclude the Relative Difference**:
- Since \( f_o^T > f_o^M \) and both \( \Delta f^T \) and \( \Delta f^M \) are positive, we can say:
\[ \Delta f^T > \Delta f^M \]
- Therefore, the relative difference of the focal lengths of the objective and eye lens in the telescope is greater than that in the microscope.

### Final Statement:
The relative difference in focal lengths of the objective and eye lens in a telescope is greater than that in a microscope:
\[ \Delta f^T > \Delta f^M \]