$A$ 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

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:

In a compound microscope,the focal lengths of the objective and eye lens are $2.5 \, cm$ and $5 \, cm$ respectively. An object is placed at $3.75 \, cm$ in front of the objective. If the final image is formed at the least distance of distinct vision,then the distance between the two lenses (length of the microscope tube) is.......$cm$.

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

$A$ 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

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.