If the focal length of the objective lens and the eye lens are $4 \, mm$ and $25 \, mm$ respectively in a compound microscope,and the length of the tube is $16 \, cm$,find its magnifying power for the relaxed eye position.

$A$ compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of the original objective lens. To retain the same magnification while keeping the object distance unchanged, the tube length has to be

The length of the tube of a microscope is $10 \, cm$. The focal lengths of the objective and eye lenses are $0.5 \, cm$ and $1.0 \, cm$ respectively. The magnifying power of the microscope is about:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: For a simple microscope,the angular size of the object equals the angular size of the image.
Reason $R$: Magnification is achieved as the small object can be kept much closer to the eye than $25\, cm$ and hence it subtends a large angle.
In the light of the above statements,choose the most appropriate answer from the options given below:

Obtain the equation of magnification for a compound microscope.

In a microscope of tube length $10 \ cm$, two convex lenses are arranged with focal lengths of $2 \ cm$ and $5 \ cm$. The total magnification obtained with this system for normal adjustment is $(5)^{k}$. The value of $k$ is . . . . . . .