Depth of Field and Focal Length in Microscopes

Depth of Field vs Depth of Focus

Depth of field is the thickness of the specimen that appears acceptably sharp at one focus setting. If you focus on the top of a cell and the bottom is blurred, the cell is thicker than the depth of field.

Depth of focus is the matching range on the image side of the lens: how far the image plane (or a camera sensor) could move while the image stays acceptably sharp.

In everyday microscopy, the two terms are often used interchangeably, and many lab manuals say “depth of focus” when they mean the specimen-side depth. This article uses depth of field for the specimen side, which is what most readers want to know about.

Why Depth of Field Shrinks at Higher Magnification

Depth of field depends mainly on the objective’s numerical aperture (NA). Higher-NA objectives collect light over a wider cone. A wide cone comes to a sharp point at only one plane and spreads quickly above and below it, so only a thin layer of the specimen looks sharp.

Because higher-magnification objectives usually have higher NA, depth of field drops sharply as you move from 4x to 10x to 40x to 100x. The same wide cone of light is also what gives high-NA objectives their better resolution, which is covered in our numerical aperture guide. Better resolution and greater depth of field pull in opposite directions.

One commonly used expression for depth of field includes a wave-optics term:

d ≈ λ × n / NA²

where λ is the wavelength of light, n is the refractive index of the medium between the specimen and objective, and NA is the numerical aperture. A fuller version adds a second term related to magnification and the resolving ability of the eye or camera. That second term matters most at low magnification.

Approximate Depth of Field by Objective

The figures below use only the wave-optics term, with 550 nm light and typical NA values. They are a guide to scale rather than precise values.

In practice, depth can seem a little greater when viewing by eye, especially at low power, because your eye can refocus slightly and because of the geometric term left out here. The overall pattern is the same: by 400x, only about a micrometer of the specimen is sharp at once, which is thinner than many cells.

Working With a Shallow Depth of Field

A shallow depth of field is a normal part of high-power microscopy, not a fault. Some ways to work with it:

• Use the fine focus constantly. At 400x and 1000x, slowly “focus through” the specimen to build a mental picture of its three-dimensional shape.
• Use lower power for thick specimens. Whole small organisms or thick sections are often better viewed at 40x or 100x.
• Make thinner preparations. Thin smears, squashes and sections put more of the specimen within the sharp zone.
• Close the condenser aperture diaphragm a little. This increases depth of field and contrast, at the cost of some resolution. A modest adjustment is often a good compromise.
• Use focus stacking for photographs. Taking several images at different focus positions and combining them in software can give a sharp image of a thicker subject.

What Focal Length Means in a Microscope

In general optics, the focal length of a lens is the distance from the lens to its focal point, where parallel incoming light comes to a focus. A shorter focal length means a stronger lens that bends light more sharply.

In a microscope, the objective and eyepiece both have focal lengths, and those focal lengths are what set their magnifications.

Objective focal length

Higher-magnification objectives have shorter focal lengths. How magnification relates to focal length depends on the microscope’s design:

• Infinity-corrected systems use a separate tube lens. The objective’s magnification is the tube lens focal length divided by the objective focal length. Tube lens focal lengths vary by manufacturer, with figures such as 180 mm and 200 mm in common use. With a 200 mm tube lens, a 10x objective has a focal length of about 20 mm and a 40x objective about 5 mm.
• Finite (often 160 mm tube length) systems, common on older and many budget microscopes, form the intermediate image directly at a set distance. Here too, a higher-power objective has a shorter focal length, roughly in proportion to its magnification.

Because of these design differences, objectives from infinity and finite systems, or from different manufacturers, are not always interchangeable.

Eyepiece focal length

Eyepiece magnification is conventionally related to focal length by:

Eyepiece magnification ≈ 250 mm / eyepiece focal length

The 250 mm figure is a standard reference viewing distance. So a 10x eyepiece has a focal length of about 25 mm, and a 20x eyepiece about 12.5 mm. The same convention appears in the formula for a simple microscope.

Finding magnification from focal length

In physics problems, the magnification of a compound microscope is often approximated as:

M ≈ (L / f objective) × (250 mm / f eyepiece)

where L is the optical tube length, the distance between the objective’s back focal point and the eyepiece’s front focal point. With L = 160 mm, an objective focal length of 16 mm and an eyepiece focal length of 25 mm, M ≈ 10 × 10 = 100x.

In day-to-day use, you don’t need this. The magnifications are engraved on the lenses, and total magnification is simply eyepiece × objective.

Focal Length vs Working Distance

These are easy to confuse:

• Focal length is an optical property of the lens system, measured from an internal reference point.
• Working distance is the physical gap between the front of the objective and the top of the coverslip when the specimen is in focus.

Working distance also gets shorter as magnification and NA increase. A 4x objective may have a working distance of well over a centimeter, while a 100x oil objective typically has a fraction of a millimeter. That is why it is important to watch from the side when raising the stage at high power, and why a slide that is too thick may not come into focus at all with the 40x or 100x objective.

Common Questions

Does the 10x or 40x objective have a shorter depth of field?

The 40x objective has a much shorter (shallower) depth of field. With typical NA values, its depth of field is a fraction of the 10x objective’s, so less of the specimen is in focus at once.

What is the focal point in a microscope?

The focal point of a lens is where parallel light rays converge after passing through it. In practice, “in focus” means the specimen sits at the position where the objective forms a sharp image at the microscope’s intended image plane, so that the eyepiece presents a sharp view to your eye.

Why do electron microscopes have greater depth of field?

Scanning electron microscopes (SEMs) form images with an electron beam that converges at a very small angle. A narrow cone like this stays nearly sharp over a much greater depth than the wide cone collected by a high-NA light objective. This is why SEM images often look strongly three-dimensional, with surfaces at very different heights all in focus.

For more on how depth of field fits into the broader picture of magnification and detail, see our guide to magnification vs resolution.