The focal length of a convex lens is 10 cm. Find its magnifying power when it is used as a magnifying glass to form the image at (i) near point and (ii) far point.

Options

A. 3.5, 2.5
B. 2.5, 3.5
C. 2.5, 1.5
D. 1.5, 2.5

Answer

To solve the problem, we need to find the magnifying power of a convex lens with a focal length of 10 cm when used as a magnifying glass. We will calculate the magnifying power for two cases: when the image is formed at the near point and when the image is formed at the far point.

### Step-by-Step Solution:

**Step 1: Understand the formula for magnifying power.**

For a convex lens used as a magnifying glass, the magnifying power (M) can be calculated using the following formulas:

1. For the near point (typically taken as 25 cm):
\[ M_1 = 1 + \frac{d}{f} \]
where \(d\) is the least distance of distinct vision (25 cm) and \(f\) is the focal length of the lens (10 cm).

2. For the far point:
\[ M_2 = \frac{d}{f} \]
where \(d\) is again the least distance of distinct vision (25 cm) and \(f\) is the focal length of the lens (10 cm).

**Step 2: Calculate magnifying power for the near point.**

Using the formula for the near point:
\[ M_1 = 1 + \frac{d}{f} = 1 + \frac{25 \text{ cm}}{10 \text{ cm}} = 1 + 2.5 = 3.5 \]

**Step 3: Calculate magnifying power for the far point.**

Using the formula for the far point:
\[ M_2 = \frac{d}{f} = \frac{25 \text{ cm}}{10 \text{ cm}} = 2.5 \]

**Step 4: State the final results.**

The magnifying power of the convex lens when used as a magnifying glass is:
- For the near point: \(M_1 = 3.5\)
- For the far point: \(M_2 = 2.5\)

### Final Answer:
- Magnifying power at near point: 3.5
- Magnifying power at far point: 2.5

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