Math and Photography

Here are some numbers for you:

  • Sensitivity: ISO 50, 100, 200, 400, 800, 1600, …
  • f/stop (size of lens opening): 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, …
  • Shutter speeds (exposure times): 1, 2, 4, 8, 15, 30, 60, 125, 250, 500, 1000, …

The first set of numbers is a range of sensor sensitivity (or film speeds, if you prefer). Each succeeding number is double the previous number, which means that half the light is needed for each step right that you go on the scale. The second set of numbers is the sequence of f/stops commonly found on camera lenses. Each succeeding number lets in half the light per unit time of the previous number. Thus f/4 lets in ½ the light of f/2.8, and ¼ the light of f/2. The third set of numbers is the set of numbers used to indicate shutter speed on most cameras. Each succeeding number exposes your sensor, whether it’s CCD, CMOS, or film, for half the time of the previous number. That third sequence should probably be written 1s, ½, ¼, 1/8, 1/15, 1/30, 1/60, 1/125, and so on, but most camera manufacturers dispense with the “1/” since it’s implied.

What does this have to do with photography? Actually, a lot. For a given light level (let’s say it’s a sunny spring or summer day), in the sun, there is an amount of light that is needed to produce a correctly exposed image. The amount of light that is needed is inversely proportional to your sensor’s sensitivity. That is, the amount of light needed goes down as your sensor’s sensitivity goes up.

There are several combinations of shutter speed and f/stop that will let in the same amount of light. For our scenario of a sunny day, with your subject (let’s say it’s your dog) in full sun, and a sensor sensitivity of ISO 200, the correct exposure would be 1/250 second at f/16. But you could also get a correct exposure at 1/125 second at f/22, or 1/500 second at f/11. Why would you want to vary your settings? Because maybe your dog is running across the yard, so you want a higher shutter speed to freeze his motion (or a lower shutter speed to show motion with blur). As you go to the right on the f/stop scale above, for each position in the sequence you go right, you must go left one position in the shutter speed sequence to get an equivalent exposure. Likewise, if you go right one position in the shutter speed sequence, you must go left one position in the f/stop sequence to get an equivalent exposure. It’s all about the math. In most cases, your camera’s built-in meter will figure this out for you automatically, but it can also be useful to take control of some of the parameters yourself!

 

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