In a simple microscope, if the final image is located at 25 cm from the eye placed close to the lens, then the magnifying power is:

Options

A. `25/f`
B. `1 + 25/f`
C. `f/25`
D. `f/25 + 1`

Answer

To solve the problem of finding the magnifying power of a simple microscope when the final image is located at 25 cm from the eye, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
In a simple microscope, there are two main components: the objective lens and the eyepiece. The final image is formed by the eyepiece, and in this case, it is located at a distance of 25 cm from the eye.

2. **Identifying the Variables**:
- Let \( D \) be the distance of the final image from the eye, which is given as \( D = 25 \, \text{cm} \).
- Let \( F \) be the focal length of the eyepiece lens.

3. **Using the Formula for Magnifying Power**:
The magnifying power \( M \) of a simple microscope is given by the formula:
\[ M = 1 + \frac{D}{F} \]
where \( D \) is the distance of the final image from the eyepiece (or the near point of the eye, typically taken as 25 cm), and \( F \) is the focal length of the eyepiece.

4. **Substituting the Known Values**:
We substitute \( D = 25 \, \text{cm} \) into the formula:
\[ M = 1 + \frac{25}{F} \]

5. **Conclusion**:
The magnifying power of the simple microscope can be expressed as:
\[ M = 1 + \frac{25}{F} \]
where \( F \) is the focal length of the eyepiece lens.

### Final Answer:
The magnifying power is \( 1 + \frac{25}{F} \).

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