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The fun stuff

A camera is a box with a hole in it. Everything else is deciding how big the hole is, how long it stays open, and what the glass in front of it does to the light.

f/2.8
Aperture and f-stops

The hole the light comes through

On a 50 mm lens, f/2.8 is a hole 18 mm across. Each step along the row is one stop: half the light of the one before. Compared with f/1.4 this lets in 1/4.

  1. N=fD
    The f-number is the focal length divided by the width of the hole. Bigger number, smaller hole.
  2. light∝1N2
    Light goes with the hole’s area. To halve the area you multiply N by √2, which is why the stops run 1.4, 2, 2.8, 4, 5.6…
Depth of field and bokeh

Why backgrounds melt

A lens is only truly sharp at one distance. A point anywhere else lands on the sensor as a small disc in the shape of the aperture. Here each distant light is a disc 1.62 mm wide on the sensor. Open the aperture and they swell into bokeh; drag the focus back and the lights sharpen while the figure dissolves.

  1. c=f2N·|d−s|d(s−f)
    The width of the blur disc for something at distance d when the lens is focused at s. Longer lens, wider aperture, or more distance between the two: more blur.
FF
Lenses

How a lens makes a picture

Drag the arrow. The image forms 105 behind the lens, upside down and 0.75× the size. That is where the sensor has to sit, and focusing is just moving the lens until it does.

  1. 1f=1u+1vm=−vu
    The thin lens equation, and the magnification. As u goes to infinity, v goes to f: distant things focus one focal length behind the lens.
Focal length

Wide, normal, long

Nothing in the scene moves when you change lens. The cabin, the tree and the walker stay at the same angles from the camera. The focal length only decides how many degrees fit across the sensor: at 35 mm a full-frame camera sees 54°. Around 50 mm looks about the way your eye does.

  1. θ=2arctan⁡(w2f)
    The angle of view for a sensor w wide (36 mm on full frame). Halve the sensor and the same lens sees half as much, which is all a “crop factor” is.
Shutter speed

Freezing time, or letting it run

Three things are moving: water falling, a windmill turning, and a wheel you can fling by swiping across the picture. At 1/125 s, the wheel at 7 m/s travels 6 cm while the shutter is open. That distance is the blur. A fast shutter freezes every drop; a slow one turns the water to silk and the windmill to a disc, which is how you show movement on purpose.

  1. blur=vtlight∝t
    Halving the time halves the blur and also halves the light: one stop, to be paid back with aperture or ISO.
  2. t=12×fps
    For video, the 180° rule: a shutter open for half of each frame gives motion the blur we are used to. At 24 frames a second that is 1/48 s.
Light

How much, and what colour

Move the lamp from 1 m to 1.5 m and the ball gets 1/2.3 of the light (1.2 stops darker). This is why a window is soft and even across a room, and a phone torch is harsh. The colour, 3200 K, is about that of a household bulb; white balance is telling the camera which of these to call white.

  1. E=Id2
    The inverse square law. Twice as far, a quarter of the light: two stops.
  2. λpeak=bT
    Wien’s law: the hotter something glows, the shorter (bluer) the wavelength it glows brightest at. So “warm” light is, confusingly, the cooler source.

Now put it together

One camera, every control from above, one living scene. Press the shutter to keep a frame.
Midday · 35 mm · focus 47.1 m
-+
Focus on

This is midday, and every scene is made up fresh, so the right settings change each time. Focus on something near at f/1.4 and watch everything behind it melt. Then f/16, and pay for it with a slow shutter that smears whatever is moving, or a high ISO that fills the shadows with grain. Press New scene for another place and another light.

Your prints will develop here.

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