Question

A converging lens of focal length $f$ is used as a simple microscope. If the least distance of distinct vision of the observer is $D$ and lens is held close to eye, magnifying power of lens is:
a)$\dfrac{D}{2f}$
b)$\dfrac{f}{D}$
c)$\dfrac{D}{f}-1$
d)$\dfrac{D}{f}$

Answer 1

The magnifying power of the lens is inversely proportional to the focal length of the lens. The bigger the focal length, the lower the magnifying power. The proportionality constant above is taken as the least distance of distinct vision.

Formula used:
$M=\dfrac{D}{f}$

Complete answer:
Let us assume the magnifying power of the lens, the focal length of the lens, and the least distance of distinct vision as $M,f, D$respectively.
Applying the values to the above formula, we get,
$M=\dfrac{D}{f}$

So, the correct answer is “Option D”.

Additional Information:
The Least distance of distance vision, also called a reference seeing distance, is the closest someone with a normal vision can comfortably look at any object or thing. Simply, it is the comfortable distance between the naked human eye and visible object. It is mathematically the product of magnifying power and the focal length of the lens. The least distance of distinct vision for the human eye is $25cm$. For infants, the least distance of distinct vision will be $7to8cm$. As a person gets old, his culinary muscles which are responsible for adjusting the eye lens get weakened due to which the least distance of distinct vision increases. This problem in old age is called presbyopia.

Note:
The least distance of distance vision for young people varies with one or two centimeters. The presbyopia is corrected for middle-aged people by wearing a bifocal lens. As the lens becomes harder and less elastic, the eye feels more difficult to focus on the object.