The objective and the eyepiece of a microscope have focal lengths of $4 \, mm$ and $25 \, mm$,respectively. The objective produces a real image $30$ times the size of the object. The final image is viewed at infinity. The near point of the microscope user is at $25 \, cm$. The overall magnification of the microscope is

$A$ compound microscope consists of an objective lens of focal length $2 \ cm$ and an eyepiece of focal length $6.25 \ cm$ separated by a distance of $15 \ cm$. How far from the objective lens should an object be placed in order to obtain the final image at the least distance of distinct vision (in $cm$)? (Take $D = 25 \ cm$).

The image formed by the objective lens of a compound microscope is:

$(a)$ $A$ card sheet divided into squares each of size $1 \; mm^2$ is being viewed through a magnifying glass (a converging lens of focal length $9 \; cm$) held close to the eye. Where should the lens be held in order to view the squares distinctly with the maximum possible magnifying power?
$(b)$ What is the magnification in this case?
$(c)$ Is the magnification equal to the magnifying power in this case? Explain.

In a Ramsden eyepiece,two planoconvex lenses,each of focal length $f$,are separated by a distance of $12 \ cm$. The equivalent focal length (in $cm$) of the eyepiece is:

$A$ person with a normal near point $(25 \;cm)$ using a compound microscope with an objective of focal length $8.0 \;mm$ and an eyepiece of focal length $2.5 \;cm$ can bring an object placed at $9.0 \;mm$ from the objective into sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.