How it works · 03
Aperture and f-numbers
Why f/2.8 lets in twice the light of f/4, why the zone of sharp focus deepens as the opening shrinks, and why stopping down too far softens everything.
Try it: aperture, light and depth of field
- Opening (focal length ÷ N)
- Light, compared with f/2.8
- In focus from … to …
- Hyperfocal distance
- Diffraction spot (Airy disk)
A ratio, not a size
The aperture is the opening light passes through. What matters for brightness is not its size alone but its size compared with the focal length, because a longer lens spreads the same light over a bigger image. The f-number is that ratio: N = f / D. A 50 mm lens with a 25 mm opening is at f/2; a 200 mm lens needs a 100 mm opening for the same f/2. Every lens at the same f-number puts the same brightness on the film, which is what lets a light meter give one reading for any lens.
Stops
Light through a circle goes with its area, so with the square of the diameter. Halving the light means dividing the area by two and the diameter by √2 ≈ 1.41. That gives the familiar sequence f/1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22: each step is one stop and halves the light. Cameras also offer half and third stops in between. The petzval lens of 1840 worked at about f/3.6, against roughly f/14 for the lens on the first daguerreotype cameras, which cut portrait exposures from minutes to under a minute.
Depth of field
A lens focuses exactly at one distance. Points nearer or further land as small blur discs, and if a disc is smaller than the eye can resolve in the final print (by convention 0.03 mm on 35mm film), the point looks sharp. A smaller opening narrows the cone of light, so the discs shrink and the depth of field grows. Focus at the hyperfocal distance and everything from half that distance to infinity looks sharp: the basis of fixed-focus snapshots from the kodak camera and brownie to the instamatic.
The diffraction limit
Stopping down has a price. Light passing an edge spreads out (diffraction), so a point never images as a point but as a small pattern, the Airy disk, about 2.44 λN across. At f/2.8 that is under 4 µm, smaller than a typical pixel; at f/22 it is about 30 µm, several pixels wide, and fine detail softens. For most lenses the sharpest setting sits two or three stops down from wide open, where aberrations have faded but diffraction has not yet taken over. A pinhole lives entirely at the diffraction end.