Three numbers that describe a microscope
When you look through a light microscope, three questions matter: how big does the image appear, how much of the sample can you see at once, and how small a detail can you actually distinguish? Each has a simple formula, and the numbers you need are engraved on the objective and the eyepiece.
Magnification
Total magnification = objective magnification × eyepiece magnification. A 40× objective with a 10× eyepiece gives 400×. Some instruments add a tube factor, for example 1.25×, which you multiply in as well.
Field of view
Field of view = field number ÷ objective magnification. The field number, in millimeters, is printed on the eyepiece, often 18, 20 or 22. With a field number of 18 and a 40× objective, you see a circle 0.45 mm across, or 450 micrometers. Doubling the magnification halves the field.
Resolution
Light spreads out as it passes through the lens, so a point becomes a small disc. Two points closer than the size of that disc blur together. The limit depends on the wavelength λ and the numerical aperture NA, engraved on the objective (for example 40/0.65):
- Abbe limit: d = λ ÷ (2 × NA).
- Rayleigh criterion: d = 0.61 × λ ÷ NA.
With green light at 550 nm and an NA of 0.65, the Abbe limit is 423 nm and the Rayleigh criterion 516 nm, about half a micrometer. A bacterium, 1 to 2 µm long, is visible; a virus, 0.1 µm, is not.
Useful magnification
Magnifying more than the objective can resolve gains nothing. The usual range of useful magnification runs from 500 × NA to 1,000 × NA: here, 325× to 650×. The 400× setting falls inside it. Above 650×, you would get empty magnification: a bigger, blurrier image.
Depth of field
A rough estimate is λ ÷ NA², here about 1.3 µm. At high magnification, only a thin slice of the sample is sharp at once, which is why you keep turning the fine focus knob.
Typical objectives
| Objective | Typical NA | Abbe limit at 550 nm |
|---|---|---|
| 4× | 0.10 | 2.75 µm |
| 10× | 0.25 | 1.10 µm |
| 40× | 0.65 | 0.42 µm |
| 100× oil | 1.25 to 1.40 | 0.20 to 0.22 µm |
Getting the best image
Use blue or green light for the finest detail, open the condenser aperture so it fills most of the objective’s aperture, and use immersion oil with oil objectives: without it, their NA drops below 1 and the resolution suffers.