What is ‘equivalence’ in exposure theory, and why is it so important?

‘Equivalence’ is a rather dry, abstract term which doesn’t really tell you anything. What it means in photographic exposure, though, is that if you change one thing, like the shutter speed, then you have to make up for it by changing another, typically the lens aperture. Equivalence is at the heart of everything your camera’s exposure system does.

• Articles on manual photography
• Manual photography: Why shoot manual at all?
• This is why manual controls on cameras matter
• How hard can it be to find an all-manual camera with actual DIALS?
• Which are the best cameras for manual exposure?
• The smartest way to get manual control is a ‘dumb’ lens

A sensor, like analog film, is a pretty simple thing. In order to record an image, sensors need to receive the right amount of light. That’s the job of your camera’s exposure controls. The amount of light the sensor requires is always the same, and it doesn’t matter if it takes a long exposure to accumulate the right amount of light or a very short one because the light is already very intense.

So the camera’s shutter speed controls how long the sensor is exposed to the image.

The lens aperture does a different job. It controls the intensity or the strength of that light passing through the lens. So between them, they control both the brightness of the light and how long the sensor is exposed to it.

The sensor doesn’t care how it’s done. It doesn’t care whether it’s a small amount of light over a long period or a large amount delivered in a fraction of a second. It’s like filling a bucket with a tap. If the water pressure is low it just takes longer – but as long as the bucket is full at the end, that’s fine.

Shutter speed vs lens aperture for exposure control

What this means for exposure control is that you have two ways of controlling the light that reaches the sensor, and you can play one off against the other. If you set a faster shutter speed then that would leave the image underexposed, so you compensate by opening up the lens aperture to let more light through. The total amount of light remains the same – and that’s ‘equivalence’.

Photographic exposure controls have been very cleverly thought out. Every full-stop aperture setting lets through twice as much light as the next (or half as much, depending on which way you’re turning the dial). Each full-step shutter speed increment also doubles or halves the light. This makes exposure calculations easy enough to do in your head.

Let’s say that you’ve figured out that the correct exposure for an outdoor scene is 1/125sec at f/8, but then you decide you need a lens aperture of f/16 to get enough depth of field. That’s two full stops of difference. So all you have to do is lengthen the exposure by two full stops – to 1/30sec – to get the same equivalent exposure.

Here’s a table that might make this clearer.

1. Let’s say your camera has indicated an exposure of 1/125sec at f/5.6. You don’t have to use this combination of shutter speed and aperture. You might start from a different shutter speed and aperture combination depending on the conditions, so this is just an example.
2. If you decide you need a different shutter speed, find it in the left column and read off the corresponding aperture on the right
3. Alternatively, find the aperture you want to use then red off the shutter speed on the left
4. The point is that all of these shutter speed and aperture combinations yield the same exposure

Shutter speed	Lens aperture
1/30sec	f/16
1/60sec	f/11
1/125sec	f/8
1/250sec	f/5.6
1/500sec	f/4
1/1000sec	f/2.8
1/2000sec	f/2
1/4000sec	f/1.4

Complicated? Kind of. But if you shoot with manual exposure controls for long enough, it soon becomes second nature. We owe a lot to the early pioneers of photography. They figured out how to make something potentially quite complicated into something rather simple. Today, we tend to make things that are really quite simple into things that are quite complicated, right?

Traditionally, exposure calculations have been based around shutter speed and aperture, and that’s it. That’s because analog film has a fixed sensitivity rating that you can’t do anything about once the film is loaded into the camera. But with digital cameras we can. We can change the ISO, or sensitivity value, from one shot to the next. This has moved us away from the two-factor simplicity of shutter speed vs aperture into the ‘exposure triangle’. Oh boy.

So why not include ISO to make the ‘exposure triangle’?

A lot of people do. ISO works on the same ‘doubling/halving’ principle too. Full-step ISO settings also double or halve the effective exposure – but note that I haven’t said they double or halve the amount of light.

That’s not how ISO works. In digital cameras, ISO is effectively a ‘gain’ control. You’re not actually increasing the amount of light forming the image on the sensor, you’re just turning up the volume. This is why higher-ISO shots have more digital noise – it’s like the hiss in low volume analog audio recordings when you turn up the volume to hear them properly.

So you CAN include the ISO setting in an ‘exposure triangle’ if you want to, and the principle of exposure equivalence still works, but now you are juggling three factors not two. The point is that where shutter speed and lens aperture control the flow and accumulation of light, the ISO setting works on the very different principle of electronic gain, and this is not quite the same thing.

There is one situation where using the ISO setting to adjust exposure can be very useful, and that’s where you need to use a minimum shutter speed to control camera shake or subject movement but the light levels are very low and you’re already shooting at the lens’s maximum aperture. Here’s a table showing how you can use ISO to manage shutter speeds in these conditions.

Shutter speed	Lens aperture	ISO
1/15sec	f/2.8	100
1/30sec	f/2.8	200
1/60sec	f/2.8	400
1/125sec	f/2.8	800
1/250sec	f/2.8	1600
1/500sec	f/2.8	3200
1/1000sec	f/2.8	6400

You can see the effect that changing the ISO setting has on the shutter speed (the aperture has been kept constant here – imagine you’re shooting wide open with an f/2.8 zoom).

1. At ISO 100, the shutter speed will be 1/15sec – camera shake is almost inevitable and any subject movement will be blurred
2. At ISO 6400 the shutter speed is 1/1000sec, so there’s no chance of camera shake and you will even be able to freeze most sports and action

The idea of ‘equivalence’ was a stroke of genius by photography’s pioneers, though treat the notion of the ‘exposure triangle’ with a certain amount of scepticism, because adding ISO into the mix for each shot makes calculations around exposure settings much more difficult to carry it out in your head because now you are juggling three variables not two, and it’s hard to think through all the permutations quickly. This is a good reason to choose an ISO suitable for the conditions and stick to it.