# lens math: focal length vs distance to subject?

I have found this illustration that shows how the framing of a subject varies at different focal lengths. At first glance, 10mm vs 17mm is quite a big difference. But then again, it seems like the photographer could just have stepped back a meter or two and have the same frame content with 17mm as with 10mm in the current position.

So I wonder ... is there a way to calculate how many meters you have to step back to fit a 10 mm frame into a 17mm focal length?

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Object size in the frame has a simple linear relationship to focal length, so if you're filling the frame at 1 meter with the 10mm lens, you'd have to step back to 1.7 meters to get the object in the frame with a 17mm lens.

It's worth pointing out that stepping back and using a longer focal length is not a direct substitute - you will end up with a different looking image. Specifically you will have less background in shot (background objects will all appear larger) and you'll have a flatter, slightly more natural looking perspective.

This technique is often used by portrait photographers who step a long way back and tend to shoot at 85mm or more. The flatter perspective is more flattering, for example the "smaller background" effect of a 10mm would make the face look smaller in comparison with the nose, thereby making the nose look bigger than it would look to the human eye.

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awesome, that simple :) so compression aside, this means for near objects i could get away with stepping back a bit. But for landscapes stepping back would mean going hundreds of meters. Makes sense. – rompetroll Sep 20 '12 at 14:24
Yeah I only bust out a the super-wide angle when I physically can't back up any more. – Matt Grum Sep 20 '12 at 14:38