If the focal length of a magnifying glass is 2.5 cm, it can magnify an object :

Question

Accepted Answer

To understand why Option 3 is the correct answer, we need to delve into the concept of magnification provided by a magnifying glass. The magnification power of a magnifying glass is determined by its focal length. The formula for calculating the magnification (M) of a simple magnifying glass is given by:

$$ M = 1 + \frac{D}{f} $$

where:
- $ D $ is the least distance of distinct vision, typically taken as 25 cm for a normal human eye.
- $ f $ is the focal length of the magnifying glass.

Given that the focal length ($ f $) of the magnifying glass is 2.5 cm, we can substitute the values into the formula:

$$ M = 1 + \frac{25}{2.5} $$

$$ M = 1 + 10 $$

$$ M = 11 $$

This calculation shows that the magnifying glass can magnify an object 11 times, which corresponds to Option 3.

Now, let's explain why the other options are incorrect:

1. **Option 1: 2.5 times** - This option is incorrect because the calculation clearly shows that the magnification is 11 times, not 2.5 times. The formula used takes into account the standard least distance of distinct vision, which results in a magnification much greater than 2.5 times.

2. **Option 2: 10 times** - This option is incorrect because, according to the formula, the magnification is 11 times. The calculation $ \frac{25}{2.5} $ results in 10, but when you add 1 (as per the formula), the total magnification becomes 11 times.

3. **Option 4: 15 times** - This option is incorrect because the calculated magnification is 11 times, not 15 times. The formula and the given focal length do not support a magnification of 15 times.

In conclusion, based on the formula for magnification and the given focal length, Option 3 is indeed the correct answer, as it accurately reflects the magnification power of the magnifying glass.