Q.Derive an expression for magnifying power of a simple microscope. Obtain its minimum and maximum values in terms of its focal length.

[!TLDR] For a simple microscope M=D/|u|, giving M_min=D/f (image at infinity) and M_max=1+D/f (image at the near point D). [!ANSWER] M_min = D/f (image at i …

A simple microscope is a single convex lens with the object placed WITHIN its focal length, forming an erect, virtual, magnified image. For small angles, tan approximately equals the angle itself, so the angular magnification is M = tan(beta)/tan(alpha) = D/|u| numerically, where u is the object's distance from the lens. Two limiting cases bound the achievable range. For MINIMUM magnifying power, the final image is placed as far as possible -- at infinity, which (from the thin-lens formula 1/f=1/v-1/u with v to infinity) corresponds to the object placed exactly at the focus, u=f numerically; substituting into M=D/|u| gives M_min = D/f. For MAXIMUM magnifying power, the final image is brought as close as the eye can still comfortably focus on it -- to the near point, v=-D; substituting v=-D into 1/f=1/v-1/u and solving for u gives u = -Df/(D+f), so |u| = Df/(D+f), and M_max = D/|u| = D(D+f)/(Df) = 1 + D/f. …

Start from M=D/|u| (small-angle approximation), then derive the two limiting object positions (u=f for image at infinity giving M_min; u=Df/(D …

Getting the two limiting cases backwards -- assuming image-at-infinity gives the MAXIMUM rather than the MINIMUM magnifying p …