The magnifiying power of a compound microscope increase with

Options

A. the focal length of objective lens is increased and that of eye lens is decreased
B. the focal length of eye lens is increased and that of objective lens is decreased
C. focal length of both objects and eye-piece are increased
D. focal lenghts of both objects and eye -piece are decreased.

Explanation

To solve the question about the magnifying power of a compound microscope, we need to understand how magnification is related to the focal lengths of the lenses involved. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding Magnification in a Compound Microscope**:
The magnifying power (M) of a compound microscope is given by the formula:
\[ M = \frac{D}{F_e} + \frac{F_e}{F_o} \]
where:
- \(D\) is the least distance of distinct vision (usually taken as 25 cm),
- \(F_e\) is the focal length of the eyepiece,
- \(F_o\) is the focal length of the objective lens.

2. **Relationship Between Focal Length and Magnification**:
From the formula, we can see that:
- The magnification increases when the focal lengths \(F_e\) and \(F_o\) decrease.
- This is because smaller focal lengths lead to larger values of \(\frac{1}{F_e}\) and \(\frac{1}{F_o}\), thus increasing the overall magnification.

3. **Conclusion**:
Therefore, to increase the magnifying power of a compound microscope, we need to decrease the focal lengths of both the eyepiece and the objective lens. This means that the correct answer to the question is that the magnifying power of a compound microscope increases with a decrease in the focal lengths of both the objective and eyepiece lenses.

### Final Answer:
The magnifying power of a compound microscope increases with the decrease in the focal lengths of both the objective and eyepiece lenses.

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