Resolution and Resolving Power of Light Microscopes

Resolution vs Resolving Power

Resolution is the smallest distance between two points that a microscope can still show as two separate points. It is expressed as a length, such as 0.5 µm or 250 nm. A smaller value is better.

Resolving power is the microscope’s ability to separate fine detail. In everyday use the two terms are often treated as the same thing. In some textbooks, resolving power is defined more strictly as the inverse of the minimum resolvable distance, so a higher resolving power means a smaller resolvable distance.

Whatever the wording, the important point is that resolution is different from magnification. Magnification makes an image bigger; resolution determines how much real detail it holds. Our magnification vs resolution guide covers that distinction in full.

Airy Disks and Why There Is a Limit

Light travels as a wave. When it passes through a circular lens opening, it spreads slightly, a process called diffraction. As a result, even a flawless objective cannot image a tiny point as a perfect point. Instead, it produces a small bright disk surrounded by faint rings, known as an Airy disk.

When two points in a specimen are far apart, their Airy disks are separate and easy to tell apart. As the points get closer, the disks overlap. At some point the overlap is so great that they look like one blurred spot. The distance at which that happens is the limit of resolution.

Two things shrink the Airy disk and so improve resolution:

• A higher numerical aperture (NA) in the objective, meaning it collects light over a wider cone. See our numerical aperture guide.
• A shorter wavelength of light.

The Formulas

You will see a few different formulas for resolution. They are not contradictory; they use slightly different definitions of when two points count as “resolved”, or different assumptions about the illumination.

Rayleigh criterion

The most commonly quoted formula is:

d = 0.61 × λ / NA

where d is the minimum resolvable distance, λ is the wavelength of light, and NA is the numerical aperture of the objective. Rayleigh’s criterion says two points are just resolved when the center of one Airy disk falls on the first dark ring of the other.

Example: a 40x objective with NA 0.65, using green light at 550 nm:

d = 0.61 × 550 nm / 0.65 ≈ 516 nm, or about 0.5 µm.

Abbe limit

Ernst Abbe’s work on image formation led to a widely used expression:

d = λ / (2 × NA)

For the same 40x/0.65 objective at 550 nm, this gives about 423 nm. The Abbe and Rayleigh figures differ somewhat but are in the same range. Both explain why, with the best oil immersion objectives (NA around 1.4) and visible light, the lateral resolution limit of a conventional light microscope is roughly 200 nm.

Including the condenser

In transmitted light, the condenser’s numerical aperture also matters. A version of the formula that includes it is:

d = 1.22 × λ / (NA objective + NA condenser)

When the condenser NA matches the objective NA, this reduces to the Rayleigh formula. If the condenser is set much lower, for example because its aperture diaphragm is closed down hard, the effective resolution gets worse.

The school-physics version

Some physics syllabuses, including those used in Indian Class 12 courses, write the limit of resolution of a microscope as:

d min = 1.22 × λ / (2 × n × sin β)

where n is the refractive index of the medium between the specimen and the objective, and β is the half-angle of the cone of light accepted by the objective. Since n × sin β is the numerical aperture, this is the same as 0.61 × λ / NA. Resolving power is then taken as 1 / d min.

How to Find the Limit of Resolution for Your Microscope

You can estimate your own objectives’ limits in a few steps:

1. Read the NA from each objective barrel. It usually follows the magnification, as in “10/0.25” or “100/1.25 Oil”.
2. Choose a wavelength. 550 nm is a reasonable figure for white light viewed by eye.
3. Apply the formula d = 0.61 × λ / NA.

These are theoretical best cases. Real results are usually somewhat worse because of lens quality, alignment, contrast and specimen preparation.

For a practical test, microscopists have long used diatoms, single-celled algae with extremely fine, regular markings on their glass-like shells. Test slides of selected diatoms, such as Amphipleura pellucida, have markings close to the limit of good oil immersion optics, so whether you can resolve them is a real-world check of both your objective and your technique.

Lateral vs Axial Resolution

The figures above describe lateral resolution: separating two points side by side in the plane you are viewing.

Axial resolution, along the optical axis (up and down through the specimen), is worse. For high-NA objectives it is commonly cited at several hundred nanometers, often quoted as roughly two to three times the lateral figure. This is one reason structures that overlap at different depths can be hard to separate, and why a shallow depth of field is a feature of high-power work. See depth of field and focal length for more.

What Affects Real-World Resolution

The formulas give an upper limit. In practice, these factors often decide what you actually see:

• Objective quality. Chromatic and spherical aberration spread light that should come to a single point. Achromat, plan achromat and apochromat objectives are progressively better corrected.
• Condenser setup. A condenser racked too low, or an aperture diaphragm closed too far, reduces the working NA.
• Coverslip thickness. Most biological objectives are corrected for 0.17 mm (No. 1.5) coverslips. High-NA dry objectives are sensitive to the wrong thickness.
• Immersion oil. Oil objectives only reach their rated NA with oil filling the gap between lens and coverslip, without bubbles.
• Contrast. Detail that is resolved but low in contrast may simply be invisible. Staining or contrast techniques can make it visible.
• The specimen. Thick or poorly prepared specimens scatter light and blur fine structures.

Practical Ways to Get Closer to the Limit

• Set up Köhler illumination if your microscope supports it, so the light is even and the condenser is properly focused.
• Adjust the aperture diaphragm for each objective. A common starting point is to open it to roughly two-thirds to three-quarters of the objective’s aperture, then adjust by eye. Closing it more increases contrast and depth but reduces resolution.
• Use a blue or green filter for slightly better resolution with stained specimens, since shorter wavelengths resolve finer detail.
• Use immersion oil correctly on 100x oil objectives, and wipe it off afterwards.
• Use the correct coverslips for your objectives.
• Keep lenses clean, especially the front lenses of the objectives and the top of the eyepieces.
• Don’t rely on more magnification. A higher-power eyepiece does not improve resolution and can lead to empty magnification.

Going Beyond the Light Microscope Limit

To resolve detail much smaller than about 200 nm, a different approach is needed:

• Electron microscopes use electrons, which have far shorter wavelengths than visible light. Modern transmission electron microscopes can resolve detail well below a nanometer.
• Super-resolution light microscopy techniques, developed in research settings, use special fluorescent labels and illumination schemes to get past the classical diffraction limit for certain kinds of specimens.

For amateur microscopy, the practical goal is usually not to beat the limit but to get as close to it as your optics allow, and the steps above go a long way toward that.