$A$ compound microscope consists of an eyepiece of focal length $6.25 \, cm$ and an objective lens of focal length $2.0 \, cm$,separated by a distance of $15 \, cm$. What is the magnifying power when the final image is formed at infinity?

Answer the following questions:
$(a)$ The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?
$(b)$ In viewing through a magnifying glass,one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?
$(c)$ Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?
$(d)$ Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
$(e)$ When viewing through a compound microscope,our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece?

The total magnification produced by a compound microscope is $24$ when the final image is formed at the least distance of distinct vision. If the focal length of the eyepiece is $5 \ cm$, the magnification produced by the objective is

In a compound microscope,the focal length and aperture of the objective lens used are,respectively:

$A$ 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

$A$ 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