$A$ compound microscope has two lenses. The magnifying power of one is $5$ and the combined magnifying power is $100$. The magnifying power of the other lens 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.

What is a compound microscope? Explain its construction with the help of a figure.

The power of two convex lenses $A$ and $B$ are $8$ diopters and $4$ diopters respectively. If they are to be used as a simple microscope,the magnification of

The focal lengths of the objective and the eye-piece of a compound microscope are $2.0 \, cm$ and $3.0 \, cm$ respectively. The distance between the objective and the eye-piece is $15.0 \, cm$. The final image formed by the eye-piece is at infinity. The two lenses are thin. The distances in $cm$ of the object and the image produced by the objective measured from the objective lens are respectively:

In a compound microscope,the intermediate image is