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

Explanation

To solve the problem of finding the magnification produced by a convergent lens (simple microscope) of power 16D when the final image is formed at the least distance of distinct vision, we can follow these steps:

### Step 1: Calculate the Focal Length of the Lens

The power \( P \) of a lens is related to its focal length \( f \) by the formula:

\[ P = \frac{1}{f} \]

where \( P \) is in diopters and \( f \) is in meters. Given that the power of the lens is 16D, we can find the focal length:

\[ f = \frac{1}{P} = \frac{1}{16} \text{ meters} \]

To convert this into centimeters:

\[ f = \frac{1}{16} \times 100 = 6.25 \text{ cm} \]

### Step 2: Use the Magnification Formula for a Simple Microscope

The magnification \( M \) produced by a simple microscope is given by the formula:

\[ M = 1 + \frac{D}{f} \]

where \( D \) is the least distance of distinct vision (typically taken as 25 cm for a normal human eye).

### Step 3: Substitute the Values into the Magnification Formula

Now, substituting the values we have:

- \( D = 25 \text{ cm} \)
- \( f = 6.25 \text{ cm} \)

The magnification can be calculated as follows:

\[ M = 1 + \frac{25}{6.25} \]

Calculating \( \frac{25}{6.25} \):

\[ \frac{25}{6.25} = 4 \]

Thus, substituting back into the magnification formula:

\[ M = 1 + 4 = 5 \]

### Conclusion

The magnification produced by the lens when the final image is formed at the least distance of distinct vision is:

\[ \boxed{5} \]

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