Confused about light intensity

[Jim Michael]

There are a couple of additional characteristics of narrow vs. broad sources to think about. First, the character of a broad light changes towards that of a narrow source as the source moves away from the subject due to the decreasing angle subtended by the light, i.e. soft lights are softest close to the subject. Second, at close distances the distance from different regions of a broad light (pythagorean theorem) results in a slight decrease in falloff with distance compared to a narrow source, i.e. moving a large source from 5.6 to 8 feet won't necessarily halve the light intensity. I can put up a Mathematica demo if anyone is interested.

[A. J. deLange]

Well, sure - strictly speaking those rules only apply to spherical spreading from a point source in an isotropic, non absorbing medium..... Nonetheless they give a pretty good picture of what is going to happen in the real world. Working the math for the example of a 2 foot wide source starting at 2 feet from a subject and then moved back to 2*sqrt(2) feet the light from the center falls off 1.0 stops. The light from an element at the edge (1 foot from the center) falls off 3/4 of a stop (including the assumption the radiator is Lambertian). Pulling back by another factor of sqrt(2) i.e. to 4 feet results in a further drop of 0.88 stop. Closer distances, emitters with narrower radiation patterns (e.g. LEDs) and bigger (wider lights) would all magnify these effects.

So the math shows the geometry has a small effect. What does the real world show? I took a Sekonic meter up to a 28" x 22" Westcott Spiderlight and backed off from 1/2 foot to 8 feet. Plotting EV vs log (base 2) of the distance and fitting from 2 feet to 8 feet shows a slope of 0.85 ± 0.065 (assuming an 0.2 standard deviation in each measurement) EV (stop) per sqrt(2) change in distance with r = -.9991 (i.e. a darn good fit). Fitting in to 1 foot shows an average change of 0.805 EV per sqrt(2) but the change from 1 foot to a half foot is only 0.25 EV per sqrt(2) change. At less than 1 foot the geometry does make a difference and the rule breaks down.


So why don't I measure 1.0 EV per sqrt(2)? There are lots of possible answers. One is that the radiant luminosity over the surface of the diffuser varies by almost an EV. Another is that the meter is out of cal. Another could be that I'm a clumsy fumbler. Most likely is that spreading isn't spherical because of reflections from the room's walls and ceiling. In any event the theory and practice both support the validity of the rule of thumb as a starting point except when very close to a large light. The only way to be sure that you have the light you want is to use an incident meter (though they too are subject to errors of a fraction of an EV (stop). Nonetheless you can be confident that if you move the closest light back by a factor of 1.4 (and it's still the closest light) you'll need about 1 extra stop of exposure and conversely.

All this is not to say that the geometric factor shouldn't be considered. It can have a measureable effect under some circumstances.