The magnifying power of a simple microscope can be increased, if we use eye-piece of

Options

A. shorter focal length is used
B. longer focal length is used
C. shorter diameter is used
D. longer diameter is used

Explanation

To solve the question regarding how to increase the magnifying power of a simple microscope, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Magnifying Power Formula**:
The magnifying power (M) of a simple microscope is given by the formula:
\[ M = 1 + \frac{D}{F} \]
where \(D\) is the least distance of distinct vision (a constant value, usually taken as 25 cm for a normal human eye) and \(F\) is the focal length of the eyepiece.

2. **Identify Constants**:
In this scenario, \(D\) is constant. Therefore, any change in magnifying power \(M\) will depend solely on the focal length \(F\).

3. **Analyze the Relationship**:
From the formula, we can see that:
\[ M \propto \frac{1}{F} \]
This indicates that magnifying power is inversely proportional to the focal length. Thus, if we want to increase the magnifying power \(M\), we need to decrease the focal length \(F\).

4. **Conclusion on Focal Length**:
To achieve a higher magnifying power, we should use an eyepiece with a **smaller focal length**. This is because a smaller focal length will result in a larger value for \(M\).

5. **Select the Correct Option**:
Based on the analysis, we conclude that the magnifying power of a simple microscope can be increased if we use an eyepiece of **shorter focal length**.

### Final Answer:
The magnifying power of a simple microscope can be increased if we use an eyepiece of **shorter focal length**.

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