$A$ microscope has an objective of focal length $1 \ cm$ and an eyepiece of focal length $6 \ cm$. If the tube length is $30 \ cm$ and the image is formed at the least distance of distinct vision,what is the magnification produced by the microscope? Take $D = 25 \ cm$.

Obtain the equation of magnification for a compound microscope.

$A$ 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?

$A$ compound microscope is used to enlarge an object kept at a distance $0.03\,m$ from its objective,which consists of several convex lenses in contact and has a focal length of $0.02\,m$. If a lens of focal length $0.1\,m$ is removed from the objective,then by what distance must the eyepiece of the microscope be moved to refocus the image? (in $cm$)

Which of the following statements are true in the context of a Compound Microscope?

We wish to make a microscope with the help of two positive lenses,both with a focal length of $20\, mm$ each,and the object is positioned $25\, mm$ from the objective lens. How far apart should the lenses be so that the final image is formed at infinity?......$mm$