Inverse Square Law
The inverse square law seems to cause a fair bit of confusion among photographers. It is pretty natural to think that if you put your flash twice as far away from your subject, you'd simply need to double the power. The idea that you need to quadruple it seems rather alien.
Try to think of it this way. If you're standing to the side of the flash, watching the light go outwards, what is happening? Well, the beam is spreading from the size of the flash outwards to cover a larger size on the wall you fire it at, right? But it is actually spreading in two directions - the horizontal direction and the vertical direction.
So when you double the distance, you're doubling the spread in both directions. So two times the distance in two directions is 4 times the area covered on the wall. So, thinking in this way, it should be quite obvious why the flash needs to be 4 times the power for twice the distance.
Click on the image below to view an animation which might help a little in visualising a 3D beam of light.
The physics bit you don't have to read
For the geeks around, you'll realise that no flash applies to the Inverse Square Law. Why? Well the Inverse Square Law only applies to a light source which shines light in all directions at equal intensity. Strobes and flashguns fire out in whatever direction they are pointed, and use reflectors to modify the way the light travels.
So is the Inverse Square Law no use? Well, if your flash gun had a huge snoot, or is focussed in some other way to the point it behaved almost like a laser, then you'd find that the Inverse Square Law would fail. However, for most situations, where light comes out the flash and gives a reasonable size beam on a wall, you'll find that the flash acts just like a little beam within a more powerful point source of light, and therefore the Inverse Square Law gives a pretty good approximation of how the light fall off will behave.
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