Three interactive lessons on the optics behind microbiology — bend light through a prism, take apart a bright-field microscope in 3D, and discover why 0.2 µm is the limit of what light can show you.
Every microscope is, at heart, a clever arrangement of lenses. To understand them, we start with how light bends.
Microscopes evolved from single polished lenses into the precise compound instruments used today.
A lens is a transparent device with two curved surfaces (glass or plastic) that uses refraction to form an image. Mirrors use curved surfaces to reflect rays and form images too.
A system of lenses/mirrors gathers rays from an object and makes them converge or diverge. The point they converge to (or seem to come from) is the image.
Visible light sits between infrared and ultraviolet on the electromagnetic spectrum — the band our eyes detect, roughly 380–760 nm. Drag to explore it.
White light is a mixture of all these wavelengths. A prism splits it into its colours because each wavelength bends by a slightly different amount.
A lens or mirror gathers the rays leaving a point on the object and makes them converge or diverge again. Wherever those rays meet — really or only apparently — is the image. Pick a case to see the rays traced.
Solid lines are real light paths. Dashed lines are not light at all — they are the backward continuations of diverging rays, drawn only to find the point the light seems to come from. An image there is virtual: you can see it through the lens, but it cannot be caught on a screen.
When light passes from one medium into another, it refracts (bends) at the interface. The refractive index (n) measures how much a substance slows light. Entering glass (higher n), light slows and bends toward the normal; leaving glass into air (lower n), it speeds up and bends away from the normal. Change the glass and the incoming angle to watch Snell's law in action.
Equilateral prism, apex angle A = 60°. Snell's law n₁ sin θ₁ = n₂ sin θ₂ is applied at both faces. Entering the glass the ray bends toward the normal (θ₂ < θ₁); leaving it bends away. δ is the total angle the prism turns the light through.
A lens acts like a collection of prisms working as a unit. When parallel rays from a distant source strike a convex lens, it focuses them at the focal point (F). The distance from the lens centre to F is the focal length (f). A shorter focal length means stronger magnification. Because our eyes can't focus closer than about 25 cm, holding a convex lens near an object lets us see it enlarged — a simple magnifier.
Real-is-positive Cartesian convention: distances are measured from the optical centre O, with the object on the left so u is negative. A positive v means a real image on the far side; a negative v means a virtual image on the same side as the object. Magnification m = v/u — negative m means the image is inverted.
Three construction rays are drawn: red travels parallel to the axis and is refracted through F₂; blue passes straight through the optical centre; violet passes through F₁ and emerges parallel to the axis. Where they meet is the image. Move the object inside the focal length and the refracted rays diverge — their dashed backward extensions then meet to form a virtual, erect, enlarged image, which is how a magnifying glass works.
The ordinary compound microscope is called a bright-field microscope because it forms a dark image against a brighter background. Rotate the model, zoom in, and click any part — or use the buttons — to learn what it does.
Light from the illuminated specimen is gathered by the objective lens, which creates an enlarged primary image inside the microscope body. The ocular (eyepiece) lens then magnifies that primary image again for your eye.
Objective and ocular work together — that's why total magnification is a product, not a sum.
The total magnification is simply the objective magnification multiplied by the eyepiece magnification.
For example, a 45× objective with a 10× eyepiece gives:
Use the calculator on the model above to try other combinations — including the 100× oil-immersion objective that reaches the practical limit of light microscopy.
Resolution is the ability of a lens to distinguish two objects that are close together as separate. More magnification is useless without it.
In the 1870s, German physicist Ernst Abbé showed that the smallest resolvable distance d between two points depends on the wavelength of light (λ) and the numerical aperture (NA = n sin θ) of the lens.
As d becomes smaller, resolution increases and finer detail is visible. That happens when the wavelength decreases and the numerical aperture increases. So the best resolution uses a large NA and short-wavelength (blue) light.
The two dots above are 0.2 µm apart (about the size of a very small bacterium). When your settings make d larger than their spacing, they blur into one; when d is small enough, they resolve into two.
Numerical aperture NA = n · sin θ, where n is the refractive index of the medium and θ is half the angle of the cone of light entering the objective. A wide cone gathers more light and separates closely packed objects; a narrow cone cannot. Widen the cone and swap air for oil to see NA rise.
Rays leave the specimen in all directions and must cross the top of the cover glass to reach the objective. Snell's law makes n·sin θ the same on both sides of that surface — so the numerical aperture is set by how steep a ray can be and still get out.
Without oil, many rays leaving the slide bend away and miss the objective. Oil bridges the slide and lens with matched refractive index, so those rays enter the lens.
The condenser also has an NA; the resolution of the whole microscope depends on both. In practice the limit is usually calculated from the objective alone using the Abbé equation.
At best a bright-field microscope separates two dots ~0.2 µm apart. Our eye can just detect a speck 0.2 mm across, so the useful limit of magnification is about 1,000 × NA.
Beyond this, "empty magnification" just enlarges a blur. Only the electron microscope has enough resolution to make higher magnifications useful.