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

$A$ scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power,he should: (Select the best option)

$(a)$ $A$ 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 compound microscope,the objective lens and eyepiece have focal lengths of $0.95 \ cm$ and $5 \ cm$ respectively,and are kept at a distance of $20 \ cm$. The final image is formed at a distance of $25 \ cm$ from the eyepiece. Calculate the magnifying power.

$A$ wire mesh consisting of very small squares is viewed at a distance of $8 \, cm$ through a magnifying converging lens of focal length $10 \, cm$,kept close to the eye. The magnification produced by the lens is

Magnifying power of a simple microscope is (when final image is formed at $D = 25 \ cm$ from eye)