Magnification, Resolution and Units

Magnification is not resolution

Magnification is how many times larger the image is than the real object. It is a pure ratio with no units, calculated from $M = I \div A$, where $I$ is the measured size of the image and $A$ is the actual size of the specimen. Resolution is something completely different: the smallest distance between two points at which they are still seen as two points rather than one blur. Magnifying an image beyond the resolving power of the instrument produces empty magnification — a bigger picture that carries no extra information.

Why the light microscope stops at about 200 nm

Resolution is limited by the wavelength of the radiation used to illuminate the specimen. Visible light has wavelengths of roughly $400$ to $700$ nm, and no instrument can resolve two points closer together than about half the wavelength it uses. This places the practical limit of a light microscope near $200$ nm. An electron beam behaves as a wave of far shorter wavelength, so a transmission electron microscope (TEM) resolves to about $0.5$ nm and reveals ribosomes, membranes in cross section and the cristae of mitochondria.

Units and the conversion that costs marks

Cambridge questions mix millimetres on the page with micrometres and nanometres in the specimen. The chain is $1\text{ mm} = 1000\ \mu\text{m} = 10^{6}\text{ nm}$. Measure the image in millimetres with a ruler, convert to the unit the answer is wanted in, then divide. A magnification written as $\times 15$ instead of $\times 15\,000$ is nearly always a missed factor of one thousand rather than a biological error.