The Short Answer
A lens magnifies by bending light. A convex lens, one that’s thicker in the middle than at the edges, bends light rays from an object inward. When the object is close to the lens, those bent rays enter your eye as if they came from a much larger object farther away. Your eye can then focus comfortably on something that takes up more of your field of view, so it looks bigger.
In other words, a magnifying lens doesn’t change the object. It changes the path of the light so the object’s image covers more of your retina. Every optical microscope, from a single hand lens to a research instrument, works on this principle.
What Refraction Is
Light travels more slowly in glass, water or plastic than it does in air. When a light ray crosses from one material into another at an angle, that change in speed makes it change direction. This bending is called refraction.
A familiar example is a straw in a glass of water, which looks bent or broken at the surface. The straw is straight. The light coming from the underwater part bends as it leaves the water, so your brain places that part of the straw in the wrong spot.
How much a ray bends depends on two things:
- The angle at which it hits the surface. A ray hitting straight on doesn’t change direction at all. The more slanted the ray, the more it bends.
- How different the two materials are. The bigger the change in light speed, the stronger the bend.
Refractive Index
The refractive index describes how much a material slows light compared with a vacuum. Air is very close to 1.0, water is about 1.33, and common optical glass is around 1.5. Higher numbers mean slower light and stronger bending at the surface.
This number matters in microscopy. Immersion oil, used with high-power objectives, is made to have a refractive index close to that of glass. That’s why it works, as explained further below.
Converging and Diverging Lenses
A lens is a piece of transparent material with curved surfaces. Because the surfaces are curved, rays hitting different parts of the lens meet the surface at different angles and bend by different amounts.
- Convex (converging) lenses are thicker in the middle. They bend parallel rays inward so they meet at a point. Magnifying glasses, microscope objectives and eyepieces all rely on converging lenses.
- Concave (diverging) lenses are thinner in the middle. They spread parallel rays outward, as if they came from a point in front of the lens. On their own they make things look smaller, but they’re often combined with convex elements inside multi-element lenses to correct errors.
Focal Point and Focal Length
If you send parallel light rays, such as sunlight, through a convex lens, they meet at a point behind it. That point is the focal point, and its distance from the lens is the focal length.
A strongly curved lens bends light more and has a short focal length. A gently curved lens has a long focal length. Shorter focal length means a more powerful lens.
Optometrists measure lens strength in diopters, which is 1 divided by the focal length in meters. A lens with a 0.25 m (25 cm) focal length is +4 diopters, and a lens with a 0.1 m (10 cm) focal length is +10 diopters.
Why Things Look Bigger: Angular Size and the Near Point
How big something looks depends on how much of your view it fills, its angular size, not on its actual size. A coin held at arm’s length can hide the moon.
So the obvious way to see more detail is to bring the object closer. The problem is that your eye can only focus so close. The closest comfortable focusing distance is called the near point, and for a typical adult it’s taken as about 25 cm (10 inches). Hold something nearer than that and it goes blurry. The near point also tends to get farther away with age.
A magnifying lens solves this problem. It lets you bring an object much closer than your near point and still see it sharply, so the object fills more of your view.
How a Magnifying Glass Makes a Virtual Image
When you place an object closer to a convex lens than its focal length, the light rays from each point of the object still spread apart after passing through the lens. They just spread apart less than before.
Your eye and brain assume light travels in straight lines. They trace those rays backward and “see” them coming from an image that’s:
- Upright, the right way round
- Enlarged
- On the same side of the lens as the object, farther away than the object really is
This is a virtual image. No light actually comes together at that location, so you can’t catch it on a screen. You can only see it by looking through the lens. Our explainer on real vs virtual images in a microscope covers the difference in more detail.
If the object sits exactly at the focal point, the rays leave the lens parallel. Your eye can then view the image fully relaxed, as if it were very far away. This is the most comfortable way to use a magnifier or a microscope eyepiece.
How Much Does a Single Lens Magnify?
A simple rule of thumb for a magnifier with your eye relaxed is:
Magnification ≈ 250 mm ÷ focal length (in mm)
The 250 mm is the standard near-point distance. So:
| Focal length of lens | Approximate magnification |
|---|---|
| 250 mm | 1x (no real gain) |
| 100 mm | 2.5x |
| 50 mm | 5x |
| 25 mm | 10x |
| 10 mm | 25x |
If you focus the image at your near point instead of at a relaxed distance, you get slightly more: about 1 + (250 ÷ focal length). Different manufacturers use one formula or the other, which is one reason magnifiers with similar lenses can be labeled differently.
The table also shows why strong magnifiers are small. A lens with a very short focal length has to be strongly curved, which in practice means a small, thick lens held close to the eye. This is how early single-lens microscopes, such as Antonie van Leeuwenhoek’s, reached high magnifications with a tiny bead-like lens. Our article on how a simple microscope works looks at that design.
Where the Image Forms Depends on the Object’s Distance
The same convex lens can make very different images depending on where the object sits. Here f is the focal length.
| Object position | Image | Example |
|---|---|---|
| Very far away | Real, inverted, much smaller, at about f behind the lens | Camera photographing a landscape; a burning glass focusing sunlight |
| Beyond 2f | Real, inverted, smaller | Camera taking a portrait |
| At 2f | Real, inverted, same size | Copying at 1:1 |
| Between f and 2f | Real, inverted, enlarged, beyond 2f | Projector; microscope objective |
| At f | Rays leave parallel; image at infinity | Eyepiece or magnifier used with a relaxed eye |
| Inside f | Virtual, upright, enlarged | Magnifying glass; microscope eyepiece |
Two rows in this table explain the compound microscope.
From One Lens to Two: The Compound Microscope
A compound microscope combines the two magnifying cases from the table:
- The objective sits a little farther from the specimen than its focal length, so it projects a real, inverted, enlarged image up the tube, much like a slide projector.
- The eyepiece is positioned so that real image sits at or just inside its focal length. It then acts like a magnifying glass, turning the real image into an enlarged virtual image for your eye.
The two magnifications multiply. A 10x objective followed by a 10x eyepiece gives 100x. Because objectives have very short focal lengths, often just a few millimeters at high power, a microscope can achieve large magnifications over a short distance. Our walkthrough of how a compound microscope works follows the full light path.
Why Real Lenses Aren’t Perfect
A single simple lens has limits that become more obvious as magnification rises. The two main problems are:
- Spherical aberration. Rays passing through the edge of a curved lens focus at a slightly different point from rays passing through the center. The result is a soft, slightly hazy image.
- Chromatic aberration. Glass bends different colors by slightly different amounts, with blue light usually bending more than red. A simple lens can’t bring all colors to the same focus, which shows up as colored fringes around edges.
Microscope objectives correct these errors by combining several lens elements made from different types of glass. Achromatic objectives are corrected for two colors and are standard on student and hobby microscopes. Apochromatic objectives are more highly corrected and more expensive. Plan objectives are also corrected so the whole field is in focus at once, not just the center.
This is why a good objective isn’t one piece of glass but a carefully designed stack of elements.
Magnification Isn’t the Same as Resolution
Lenses can enlarge an image almost without limit, but that doesn’t mean you’ll see more. What matters is resolution: the ability to show two close points as separate.
Light behaves as a wave, and as it passes through a lens it spreads slightly (diffraction). That blurs every point into a tiny spot and sets a limit on the finest detail any lens can show. The limit depends on two things:
- The wavelength of light. Shorter wavelengths, toward blue, give slightly better resolution.
- The numerical aperture (NA) of the objective. NA measures how wide a cone of light the lens can collect. A wider cone carries finer detail. NA is engraved on each objective.
A widely used approximation is that the smallest resolvable distance is about the wavelength divided by twice the NA. For green light (about 550 nm) and a high-quality oil-immersion objective with an NA of 1.4, that works out to roughly 0.2 µm. This is why ordinary light microscopes can’t resolve objects such as viruses, however much they magnify. Going beyond that limit needs different techniques, such as electron microscopes, which our comparison of light vs electron microscopes covers.
Enlarging the image beyond what the resolution supports is called empty magnification. The picture gets bigger, but no new detail appears.
Why Immersion Oil Helps
Here’s where refraction comes back in. When light leaves the glass slide and coverslip and enters air, it bends sharply, and the most steeply angled rays miss the objective entirely. Those steep rays carry the finest detail.
Immersion oil has a refractive index close to glass (typically about 1.515). With a drop of oil filling the gap between coverslip and objective, the light passes through without bending much at that boundary. The objective collects a wider cone of light, its NA rises above 1, and the image shows finer detail. This only works with objectives designed for oil, usually marked “Oil” or “Oel”.
Try It Yourself
A few simple experiments make these ideas concrete:
- Water-drop lens. Put a small drop of water on a piece of clear plastic and hold it just above printed text. The curved drop acts as a tiny convex lens and magnifies the letters. A smaller, rounder drop has a shorter focal length and magnifies more.
- Find the focal length. Stand on the far side of a room from a bright window, facing it, and hold a sheet of white paper up. Hold a magnifying glass between the window and the paper, and move it toward or away from the paper until a small, sharp, upside-down image of the window appears. That’s a real image, and the distance from lens to paper is close to the focal length. (Don’t do this with direct sunlight, and never look at the sun through a lens.)
- Watch the image flip. Look at a distant object through a magnifying glass held at arm’s length. It appears upside down: you’re seeing a real image. Bring the lens toward something close and it becomes upright and enlarged: now you’re seeing a virtual image.
These are the same two behaviors that the objective and eyepiece rely on inside every compound microscope. For more on the basic ideas and vocabulary, see our introduction to microscopy.