Simple Microscope: Magnifying Power

A simple microscope, more commonly called a magnifying glass, is nothing more than a single convex lens of short focal length, used to view a small object placed within its focal length, so that the lens forms a virtual, erect, magnified image of the object, which the eye then views comfortably. Two closely related magnifying-power formulas are used, depending on exactly where the eye chooses to focus this virtual image. If the lens is held so that the virtual image forms exactly at the eye's near point $D$ (the most common way a magnifying glass is actually used, since this is where the unaided eye can see the sharpest detail), then applying the thin lens formula with $v=-D$ and using the definition $M=\beta/\alpha\approx\tan\beta/\tan\alpha$ for the small angles involved gives $M=1+\frac{D}{f}.$ Alternatively, if the lens is held so that the object sits exactly at its focus, so that the emergent rays are parallel and the (now relaxed, unaccommodated) eye views the virtual image formed at infinity -- generally the more comfortable way to use a magnifier for any length of time, since the eye is not straining to accommodate -- the magnifying power comes out slightly smaller, as $M=\frac{D}{f}.$ In both cases the magnifying power is larger the shorter the lens's focal length $f$ is, which is exactly why a physically small, strongly-curved magnifying lens magnifies more than a large, gently-curved one, and why a simple microscope's magnifying power …