Magnifying power of simple microscope is $6$, when image is formed at distance of distinct vision, the focal length of simple microscope is:
A) $15cm$
B) $25cm$
C) $5cm$
D) $4.16cm$

Hint: In order to solve this problem you have to know the concept of simple microscope, also the formula for finding the magnification power of a simple microscope. Remember that the value of least distance of the distinct vision is $25cm$.

Formula used:
The formula for finding the magnification power of simple microscope is given as
$m = 1 + \dfrac{D}{f}$
Where, $D$ is the least distance of the distinct vision
$f$ is the focal length of the lens

Complete step by step solution:
It is given that the magnification power of the simple microscope is
$m = 6$
And as we know that the least distance of distinct vision is given as
$D = 25cm$
Now, we have to find the focal length of the simple microscope, when the image is formed at a distance of at least distance.
For this, we have to apply the formula for finding the magnification power of simple microscope which is given as
$m = 1 + \dfrac{D}{f}$
Where, $D$ is the least distance of the distinct vision
$f$ is the focal length of the simple microscope
Now, on putting all the values in the above formula, we get
$ \Rightarrow 6 = 1 + \dfrac{{25}}{f}$
On further solving, we get
$ \Rightarrow 5 = \dfrac{{25}}{f}$
From the above relation, find the value of focal length, we get
$ \Rightarrow f = \dfrac{{25}}{5}cm$
On further solving, we get
$f = 5cm$
Hence, the focal length of the simple microscope, when the image is formed at a distinct of least distance is $5cm$.
Therefore, the correct option is (C).

Additional Information:
There are the various uses of simple microscope:
1. It is used in the study of soil particles (pedology).
2. It is used for finding the various skin diseases by a dermatologist.
3. It is used for the study of microorganisms such as algae, fungi etc.
4. It is also used in the jewellery shops to get a magnifying image of a very small part of jewellery.

Note: Remember that the simple microscope has one objective lens whereas a compound microscope has two to four objective lenses. Also the concave reflecting type mirror is used in the simple microscope while in compound microscope, on one side plane mirror and on the other side concave mirror is used.