The chance of taking a blink-free photo
Nic Svenson does the maths of the probability of a blink being captured by a camera's shutter.
Nic Svenson: In my line of work, writing about physics, I often end up being the photographer as well, and because science is a team sport I'm called upon to do a lot of group shots. If you've ever been the designated photographer at an important family function, you'll know what I'm about to say. Even if everyone stays perfectly still, there's always someone who blinks. I wondered just how many photos I have to take in order to get at least one where no one's blinking. So I started counting people, photos, photos spoiled due to blinks. It was taking forever. I can't make up a rule after ten counts. To be what's known as statistically significant I'd need at least a couple of hundred. I whinged about this to one of my physics colleagues, Dr Piers Barnes, and he said, 'You don't need data. We can model it.'
Trying not to feel like an idiot for thinking science is based on hard numbers, I set about finding some figures to plug into the formula Piers was working on at lunchtime...well, I hope it was just his lunchtime. I found that the average number of blinks made by the average person when doing something slightly stressful, like getting their photo taken, is ten per minute. The average blink lasts about 250 milliseconds from when the lid starts to close to when it's fully reopened, and the shutter on my camera stays open for about eight milliseconds if I'm indoors in good light. (1 - x)
Figuring out the number of photos to take so I can expect to get one where no one's blinking relies on probabilities. When sorting out probabilities of events you have to consider what might influence them. For our purposes I reckon it's fair to say that blinks are independent. If a group of people are looking at a camera, one person's blinks won't influence another's and, unless you've got something caught in your eye, your blinks don't influence each other either. It's also safe to say that blinks are random; they certainly don't happen every six seconds. This means we're looking for the probability of a random event, a blink, occurring during a window of time, how long the shutter is open, that's much shorter than the event itself.
Although the formulae of calculating probabilities look quite daunting, the same components keep cropping up. This meant Piers could do a lot of cancelling out, simplifying his job and mine. Piers says the probability of someone spoiling a photo by blinking equals their expected number of blinks, which we'll call x, multiplied by the time during which the photo could be spoilt t. He says this works only if the expected time between blinks is longer than the time when a photo could be spoilt, which it is. This makes the probability of one person not blinking is:
(1 - xt)
The probability of two people not blinking is:
(1 - xt) (1 - xt)
That's squared. For three people it's cubed, and so on. So let's test this.
Each shutter opening results in either a good photo or a spoilt one, and if you plot a whole lot of these successes and failures on a graph, you'll find it follows what statisticians call the normal distribution. You've probably heard of the bell curve. Well, that's what the normal distribution looks like. At one end of the bell curve the photographer got all good shots. In the middle of the curve the number of good and bad photos is split 50/50. At the other end are all dud trials; the photographer got no good shots. Piers then figured out how many shots I'd need to be 99% certain of getting a good one. He found that photographing 30 people in bad light would need about 30 shots. And once you've got around 50 people, even in good light, you can petty much kiss your hopes of an unspoilt photo goodbye.
So here's the rule of thumb for calculating the number of photos you have to take of groups less than 20: divide the number of people by three if there's good light, and by two if the light is bad. Who said physicists are no good at solving everyday problems?
- Nic Svenson
- Communications Officer
CSIRO Industrial Physics
Fax: +61 (2) 9413 7644
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