Home > Photography Tips/Tricks > Inverse Square Law – A Photographers Take

Inverse Square Law – A Photographers Take


Seldom would you think that physics comes into play with photography. But you’d be wrong. In fact, the Inverse Square Law states that the intensity of point light source is inversely proportional to the square of the distance from the source. (Say what?!) This means an object twice as far away from the source receives only 1/4 of the light. But this also means that the greater the distance from the source, the less change over a given distance.

However, this is where it gets tricky…


So lets say you have a studio light set up and measured the output directly at the source and again at 2, 4, 8 and 16 feet. At two feet lets imagine you metered the light at F16. But each time you double the distance from the light source, the intensity drops off by FOUR TIMES as much or two full f-stops. This means at four feet the light will meter only F8 (which is 2 f-stop or 4x less than at 2 feet). And at eight feet it will meter F4 which again is 2 f-stop or 4x less than at 4 feet. And at sixteen feet the light will only meter F2 and is now a full 6 stops less than your meter reading at 2 feet. But take note here that each distance measurement is doubling meaning that the farther from the source you get, the less the light drops off per increase in distance.

Lets me set up an example of what makes knowing the Inverse Square Law important as a photographer. Imagine you are hired to photograph your Uncle Bob and Aunt Sophie in your studio. You decide to pose Uncle Bob just behind and to the right of Aunt Sophie and place the main light source only two feet in front of her and to the the camera left. And lets say that Uncle Bob is roughly two feet further from the light source. This means to expose for Aunt Sophie will result in Uncle Bob being underexposed by 2 f-stops because only 1/4 the light intensity is hitting him compared to her. And to expose for Uncle Bob would result in her being over exposed by the same 2 f-stops. That’s not going to be a keeper!

We should try this again, but this time with the light source 16 feet from Aunt Sophie and Uncle Bob is still roughly two feet further from the source. This means that the intensity of the light hitting Aunt Sophie is going to be considerably less than with the light placed only 2 feet from the couple as above. But because of the change in distance, the intensity of the light isn’t going to drop another full f-stop until you get 24 feet away or 2 f-stop at 32 feet. Meaning Uncle Bob standing 18 feet from the light is going to be roughly a 1/4 f-stop lower than Aunt Sophie. Whoa! That’s like magic or something!

Of course the side effects of moving the light away is that it now becomes a “smaller” light source AND you will need more power to light them with the same camera settings as you would with the light source closer. As for the size of the source, it doesn’t actually shrink. Instead it is smaller in relation to your subject due to the increased distance from your subject. (Although the Sun is 865,000 miles in diameter, it appears as only a small dot in the sky due to its distance from Earth.) As with any “small” light source, the shadows will become more defined and the light will “wrap” around the subject less resulting in it appearing as a higher contrast light source. We could counteract this by using a physically larger source and/or by increasing the relative size of the source with a larger soft box or umbrella. Of course that has its limitations due to available space and larger modifiers are often more expensive. As for the reduction in output with the increased distance, that will all depend on your flash and if it has the power to compensate. Otherwise you would need to adjust the camera settings by increasing the ISO value or using a larger aperture. Or for constant light sources such as a tungsten light, you can use a slower shutter speed to compensate as well. But when using a flash as the primary light source, the shutter speed will only affect any constant or ambient lights that may be present. (There is a lesson to learn here as well, you can blend ambient with flash by dragging the shutter and get some interesting results in dim rooms or outdoors at night.)

But wait, the distance doubles but the light intensity drops by one-quarter? That doesn’t make sense… Shouldn’t it drop by only half? Nope. Here’s why:

The diagram above shows, the light will both cut in intensity by one-quarter BUT it will then cover 4 times the area as it did at half the distance. So if we imagine that the first square is a wall one square foot in size and 4 feet from the source, the second wall is 8 feet from the source and light will have spread over a 4 square foot area at 1/4 the intensity of the first wall. And a wall at 16 feet, or double the distance from the second wall, the light will be again 1/4 the intensity but again now covers 4 times as much area (or 16 times as much as at 4 feet).

Imagine it like this. The light is spreading out like water out of a hose spray nozzle. The intensity and stream of water right out of the sprayer is strong and will soak a person at point-blank range but spray someone 20 feet away and it will only feel like a slight shower to them. Of course you could focus the stream of water as could you with the light which would result in throwing the light farther with the same amount of power BUT inverse square still applies.

In any case, hopefully this clears up some of the confusion about how it works and what it means for photographers. So don’t be afraid to move those lights around to help even out the light or to create more contrast between your subject and the background.

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  1. Zim
    January 21, 2010 at 9:10 am

    Excellent article, thank you 🙂

  2. Ian
    February 1, 2010 at 7:18 pm

    The one comment I would have is that, as you so rightly pointed out in the opening paragraph, the inverse square law only applies to POINT light sources – generally defined as one from which the light can emanate in all directions and has a relatively low surface area compared to the light output. A studio light is a light bulb (point source) but also will be in a shade of some sort, which is generally reflective and so the inverse square law does not apply, and in fact you need to treat it as a plane source approximation, assuming that almost all of the light is emanating from one side of the light. Otherwise, a brilliant article and a good description of the inverse square law.

    Yours,
    Ian, Medical Physicist, UK

    • modifiedphoto
      February 1, 2010 at 8:04 pm

      Thanks, from what I’ve found it does apply to enough of an extent that the results work in much the same way. (Perhaps to a less exact measurement than for a point source but closely enough for photographers to work with.)

      I would set up a light and test how it reacts with a diffusion material (such as a box or umbrella) but I simply don’t have the space or really the time. Perhaps one day I will and will post my results then.

  3. Henry Katz
    December 25, 2010 at 8:05 pm

    I would point out that the same applies within lenses. The light source may then be taken as the light falling on the lens’ front. A 50mm lens at f4 (diameter of 50/4 = 12.5mm) will focus that light with the same intensity as does a 100mm lens at f8 (diameter of 100/8 = 12.5mm) only if light from the longer lens falls on the receptor for 4 x the time.

    HK

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