Q.Explain what is meant by the magnifying power of a simple microscope (magnifying glass), and derive the expression $M=1+\dfrac{D}{f}$ for the case when the final image is formed at the near point.

A simple microscope (magnifying glass) is a single short-focal-length convex lens, used to view an object placed within its focal length so the lens forms a virtual, erect, magnified image. Magnifying power $M$, defined as the ratio of the angle the final image subtends at the eye to the angle the object itself would subtend viewed unaided from the near point, works out to $M=1+D/f$ when the virtual image is thrown to the near point $D$, or the slightly smaller $M=D/f$ when the object sits exactly at the focus so the (relaxe …