$A$ microscope has an objective of focal length $2 \ cm$,an eyepiece of focal length $4 \ cm$,and a tube length of $40 \ cm$. If the distance of distinct vision is $25 \ cm$,the magnification of the microscope is:

The least distance of distinct vision is $25 \ cm$. Find the magnifying power of a simple microscope of focal length $5 \ cm$ if the final image is formed at the least distance of distinct vision.

In a compound microscope,the magnified virtual image is formed at a distance of $25 \, cm$ from the eye-piece. The focal length of its objective lens is $1 \, cm$. If the magnification is $100$ and the tube length of the microscope is $20 \, cm$,then the focal length of the eye-piece lens (in $cm$) is

$A$ simple microscope is used to see an object first in blue light and then in red light. Due to the change from blue to red light, its magnifying power

The focal length of the objective lens and the eyepiece of a microscope are $2 \, cm$ and $5 \, cm$ respectively,and the distance between them is $20 \, cm$. Find the distance of the object from the objective lens when the final image is seen by the eye at $25 \, cm$ from the eyepiece.

$A$ student measures the thickness of a human hair by looking at it through a microscope of magnification $100$. He makes $20$ observations and finds that the average width of the hair in the field of view of the microscope is $3.5 \; mm$. What is the estimate on the thickness (in $mm$) of hair?