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 magnification for relaxed eye viewing?

Answer

To find the magnification for relaxed eye viewing using a converging lens with a focal length of 12 cm, we can follow these steps:

### Step 1: Understand the Concept of Magnification
Magnification (M) in the case of a simple microscope (converging lens) is defined as the ratio of the distance of the image (v) from the lens to the distance of the object (u) from the lens. However, for relaxed eye viewing, we use a specific formula.

### Step 2: Use the Formula for Magnification
For relaxed eye viewing, the magnification (M) can be calculated using the formula:
\[ M = \frac{d}{f} \]
where:
- \( d \) is the least distance of distinct vision (typically taken as 25 cm for a normal eye).
- \( f \) is the focal length of the lens.

### Step 3: Substitute the Values
Given:
- \( d = 25 \) cm (least distance of distinct vision)
- \( f = 12 \) cm (focal length of the lens)

Now, substituting these values into the formula:
\[ M = \frac{25 \, \text{cm}}{12 \, \text{cm}} \]

### Step 4: Calculate the Magnification
Now, perform the division:
\[ M = \frac{25}{12} \approx 2.0833 \]

### Step 5: Round the Result
For practical purposes, we can round this to:
\[ M \approx 2.1 \]

### Final Answer
Thus, the magnification for relaxed eye viewing is approximately **2.1**.

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