A convergent lens of power 16D is used as a simple microscope. The magnification produced by the lens, when the final image is formed at least distance of distinct vision is

Options

A. 6
B. 4
C. 7
D. 5

Answer

To find the magnification produced by a convergent lens of power 16D when the final image is formed at the least distance of distinct vision (25 cm), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Power of the lens (P) = 16 D
- Least distance of distinct vision (D) = 25 cm

2. **Calculate the focal length (f) of the lens:**
The relationship between the power (P) and the focal length (f) is given by:
\[ P = \frac{1}{f} \quad \text{(in meters)} \]
Rearranging the formula gives:
\[ f = \frac{1}{P} \]
Substituting the value of P:
\[ f = \frac{1}{16} \text{ m} = 0.0625 \text{ m} \]
Converting this to centimeters:
\[ f = 0.0625 \text{ m} \times 100 \text{ cm/m} = 6.25 \text{ cm} \]

3. **Use the formula for magnification (M) of a simple microscope:**
The magnification produced by a simple microscope when the image is formed at the least distance of distinct vision is given by:
\[ M = 1 + \frac{D}{f} \]
Where D is the least distance of distinct vision and f is the focal length. Substituting the values:
\[ M = 1 + \frac{25 \text{ cm}}{6.25 \text{ cm}} \]

4. **Calculate the magnification:**
\[ M = 1 + 4 = 5 \]

5. **Conclusion:**
The magnification produced by the lens is:
\[ M = 5 \]

### Final Answer:
The magnification produced by the lens is **5**.