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

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

$A$ simple microscope is a combination of two lenses in contact. Their powers are $+20$ $D$ and $-4$ $D$. The distance of distinct vision is $25$ cm. When seen through the microscope, the size of an object $3$ mm high is (in $cm$)

Which of the following statements are true in the context of a Compound Microscope?
$(A)$ Each lens produces a virtual and inverted image.
$(B)$ The objective has a very short focal length.
$(C)$ The eyepiece is used as a simple magnifying glass.
$(D)$ The objective and eyepiece are convex and concave lenses respectively.

$A$ microscope has an objective of focal length $2 \ cm$,an eyepiece of focal length $4 \ cm$,and a tube length of $40 \ cm$. If the distance of distinct vision is $25 \ cm$,the magnification of the microscope is:

The focal lengths of the objective and eye-lens of a microscope are $1 \,cm$ and $5 \,cm$ respectively. If the magnifying power for the relaxed eye is $45$,then the length of the tube is $....... \,cm$.