The focal lengths of the objective and the eyepiece of a compound microscope are $2 \,cm$ and $3 \,cm$ respectively, and the distance between them is $15 \,cm$. The final image formed by the eyepiece is at infinity. The distances of the object and the image produced by the objective lens from the objective lens are respectively:

$(a)$ $A$ 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.

Which type of electromagnetic waves are used in an optical microscope? Why?

In which of the following is the final image erect?

$A$ simple magnifying lens is used in such a way that an image is formed at $25 \, cm$ away from the eye. In order to have $10$ times magnification,the focal length of the lens should be

$A$ card sheet divided into squares each of size $1\,mm^2$ is being viewed at a distance of $9\,cm$ through a magnifying glass (a converging lens of focal length $9\,cm$) held close to the eye. What is the angular magnification (magnifying power) of the lens?