Microscope magnification and resolution

A microscope produces an image of an object. Magnification tells us how many times larger the image is than the real object. It compares a length on the image with the corresponding real length.

\text{magnification} = \frac{\text{size of image}}{\text{size of real object}}

The image size and real size must be expressed in the same units before calculating the ratio. Magnification itself has no units: a magnification of $\times 400$ means that each measured length on the image is 400 times the corresponding real length.

Calculating image size and real size

For an object viewed with an optical microscope, measure a length on its image and divide by the magnification to find the corresponding real length. The same relationship can be rearranged to find image size.

\begin{aligned} \text{real size} &= \frac{\text{image size}}{\text{magnification}} \\ \text{image size} &= \text{real size} \times \text{magnification} \end{aligned}

For example, if an image is $20\ \text{mm}$ long at a magnification of $\times 400$ , the real object is $20\ \text{mm} \div 400 = 0.05\ \text{mm}$ long. This is also $50\ \mu\text{m}$ .

Resolution and visible detail

Resolution is the ability to distinguish two close points as separate. A microscope with a smaller minimum distinguishable distance has better resolution: it can distinguish points that are closer together.

Magnification makes an image larger, but resolution determines how much detail can be distinguished. Enlarging an image beyond its resolution limit makes the existing image bigger without revealing additional detail.