What Numerical Aperture Is
Numerical aperture (NA) is a number that describes how wide a cone of light a microscope objective can collect from the specimen. It has no units. Typical values range from about 0.1 on a low-power objective to around 1.4 on high-end oil immersion objectives.
NA matters because it sets the limit on how much detail an objective can resolve. Two objectives with the same magnification but different NA can show noticeably different amounts of detail. That is why NA is sometimes called the most important number on an objective, and why it explains so much of the difference between magnification and resolution.
The Formula
NA = n × sin θ
- n is the refractive index of the medium between the specimen (or coverslip) and the front lens of the objective.
- θ is half the angle of the cone of light that the objective can accept. The full angle is called the angular aperture.
Approximate refractive indices for common media:
| Medium | Refractive index (n) |
|---|---|
| Air | about 1.00 |
| Water | about 1.33 |
| Glycerol | about 1.47 |
| Standard immersion oil | about 1.515 |
Example: a dry objective (in air) that accepts a cone with a half-angle of 30° has NA = 1.0 × sin 30° = 1.0 × 0.5 = 0.5.
A wider cone (larger θ) gives a higher NA. So does a medium with a higher refractive index.
Why Immersion Oil Raises NA
In air, n is about 1, and sin θ can never exceed 1, so a dry objective’s NA is always below 1. In practice, the highest NA for dry objectives is about 0.95, because lenses cannot collect light at angles approaching a full 90° from the axis.
When light leaves the coverslip into air, it bends sharply at the glass-air boundary. Some of the most steeply angled rays, which carry the finest detail, are bent so much that they miss the objective or are reflected back.
Immersion oil is chosen to have a refractive index close to that of glass. With oil filling the gap between coverslip and objective, light passes from glass to oil to lens with very little bending, so those steep rays reach the objective. This raises n in the formula and allows NA values above 1, commonly around 1.25 to 1.4.
The practical consequence: an oil immersion objective used without oil performs poorly. It cannot reach its rated NA, and the image is typically dim and blurred.
Typical NA Values
NA depends on both magnification and the objective’s optical grade. The figures below are typical examples; exact values vary between manufacturers.
| Magnification | Achromat | Plan achromat (typical) | Plan apochromat (typical) |
|---|---|---|---|
| 4x | 0.10 | 0.10 | 0.16 to 0.20 |
| 10x | 0.25 | 0.25 | 0.40 to 0.45 |
| 20x | 0.40 | 0.40 | 0.75 to 0.80 |
| 40x | 0.65 | 0.65 | 0.90 to 0.95 |
| 100x oil | 1.25 | 1.25 | 1.40 to 1.45 |
Standard achromats, the type supplied on most student and hobby microscopes, follow the left-hand column closely. Higher-grade objectives offer more NA at the same magnification, which is a large part of why they cost more.
How to Read NA on an Objective
NA is usually engraved right after the magnification, separated by a slash or a space:
- 10/0.25: 10x magnification, NA 0.25.
- 40/0.65 160/0.17: 40x, NA 0.65, designed for a 160 mm tube length and 0.17 mm coverslips.
- 100/1.25 Oil: 100x, NA 1.25, requires immersion oil.
- 40x/0.75 ∞/0.17: 40x, NA 0.75, infinity-corrected, 0.17 mm coverslips.
Objectives labelled “Oil”, “Oel”, “HI” (homogeneous immersion) or with a black ring need oil. “W” or “Water” means water immersion.
What NA Controls
Resolution
The smallest detail an objective can separate is approximately:
d = 0.61 × λ / NA
where λ is the wavelength of light. With green light at 550 nm, an NA 0.65 objective resolves about 0.52 µm, and an NA 1.25 objective about 0.27 µm. Higher NA, finer detail. The formulas and their variations are covered in resolution and resolving power.
Useful magnification
A common rule of thumb is that total magnification is useful between about 500 × NA and 1000 × NA. Beyond the upper end, the image grows without gaining detail. For a 40x/0.65 objective, that suggests roughly 325x to 650x total. See empty magnification for more.
Brightness
A higher NA objective gathers light from a wider cone, so it can collect more light from the specimen. Image brightness also depends on magnification, though, since higher magnification spreads the collected light over a larger image. At the same magnification, a higher-NA objective generally gives a brighter image.
Depth of field and working distance
Higher NA comes with trade-offs:
- Shallower depth of field. Less of the specimen’s thickness is in focus at once. Our article on depth of field and focal length gives approximate figures.
- Shorter working distance. High-NA objectives often sit very close to the coverslip.
- More sensitivity to coverslip thickness. High-NA dry objectives, such as 40x/0.95, can be noticeably affected by coverslips that differ from the designed 0.17 mm. Some have a correction collar for this.
The Condenser Counts Too
In transmitted-light microscopy, the condenser below the stage also has a numerical aperture, often engraved on it (a common Abbe condenser is NA 1.25). The condenser’s working NA depends on its height and how far its aperture diaphragm is opened.
If the condenser is lowered or its diaphragm is closed far down, the cone of illuminating light narrows, and the effective resolution falls even if the objective has a high NA. On the other hand, opening the diaphragm fully can wash out contrast in unstained specimens.
A common starting point is to open the aperture diaphragm to roughly two-thirds to three-quarters of the objective’s NA, then adjust by eye for the best balance of detail and contrast. Re-adjust it every time you change objectives.
To use a condenser above about NA 1.0 to its full extent, oil is needed between the condenser and the underside of the slide as well. Most amateurs don’t do this routinely, and it is not necessary for most viewing.
Practical Tips for Amateur Microscopists
- Compare objectives by NA, not just magnification, when buying or upgrading.
- Always use oil with oil immersion objectives, and clean it off the lens after use with lens tissue.
- Keep the condenser raised close to the slide for higher powers on most student microscopes.
- Adjust the aperture diaphragm for each objective rather than leaving it in one position.
- Use coverslips of the thickness your objectives are designed for, usually 0.17 mm (No. 1.5).
- Don’t chase total magnification with stronger eyepieces. Past about 1000 × NA, extra magnification is unlikely to help.