A detective uses a converging lens of focal length 12 cm to examine the fine details of some cloth fibers found at the scene of a crime.
What is the maximum magnification given by the lens?

Answer

To find the maximum magnification given by a converging lens with a focal length of 12 cm, we can use the formula for magnification in the case of a simple microscope:

### Step-by-Step Solution:

1. **Understand the Concept of Maximum Magnification**:
The maximum magnification (M) of a lens occurs when the final image is formed at the least distance of distinct vision (D), which is typically taken as 25 cm for a normal human eye.

2. **Identify the Given Values**:
- Focal length of the lens (f) = 12 cm
- Least distance of distinct vision (D) = 25 cm

3. **Use the Magnification Formula**:
The formula for maximum magnification for a simple microscope is given by:
\[ M = 1 + \frac{D}{f} \]

4. **Substitute the Values into the Formula**:
\[ M = 1 + \frac{25 \text{ cm}}{12 \text{ cm}} \]

5. **Calculate the Fraction**:
\[ \frac{25}{12} \approx 2.0833 \]

6. **Add 1 to the Result**:
\[ M = 1 + 2.0833 \approx 3.0833 \]

7. **Final Result**:
The maximum magnification is approximately 3.08, which can be rounded to 3.1 for practical purposes.

### Conclusion:
The maximum magnification given by the lens is approximately **3.1 times** the height of the object.

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