In a simple microscope, if the final image is located at infinity then its magnifying power is

Options

A. (a)`25/f`
B. (b)`D/25`
C. (c)`f/25`
D. (d)`f/D^(+1)`

Answer

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

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A simple microscope consists of a convex lens.
- When the final image is at infinity, the object must be placed at the focal point of the lens.

2. **Identifying the Least Distance of Distinct Vision**:
- The least distance of distinct vision (D) is typically taken as 25 cm for a normal human eye.

3. **Using the Formula for Magnifying Power**:
- The magnifying power (M) of a simple microscope is given by the formula:
\[ M = \frac{D}{F} \]
where:
- \(D\) is the least distance of distinct vision (25 cm).
- \(F\) is the focal length of the lens.

4. **Setting the Condition for Final Image at Infinity**:
- For the image to be at infinity, the object must be placed at the focal length (F) of the lens.
- Therefore, we can substitute the values into the magnifying power formula.

5. **Final Calculation**:
- Substituting \(D = 25 \, \text{cm}\) into the formula:
\[ M = \frac{25}{F} \]
- This means that the magnifying power depends on the focal length of the lens used in the microscope.

6. **Conclusion**:
- The magnifying power of the simple microscope when the final image is at infinity is \(M = \frac{25}{F}\).