In my article on Apparent Light Size, we saw the differences in light produced by large and small light sources. I demonstrated this by starting with a flash in a small softbox set up very close to a small object, therefore making a large light source. I then moved the light farther and farther away, thereby simulating a smaller light source. The actual light size didn't change, but its apparent size did in relation to the subject. I noted at the end of the post that as the light source got farther away, the background began to get brighter. The reason for that is something that I've struggled with in learning to light, and it's called the inverse square law.
Now before you go surfing away I'm going to put out there that math and me are not friendly. Seriously, I jumped the shark in tenth grade algebra, so the minute this little aspect of lighting came up it was a challenge for me to grasp. Fractions. Equations. Physics...I just wanted to make photographs.
But here's what I'll tell you. Read about the inverse square law here and on the web and don't let it confuse you. Just get familiar with it. Then bust out your camera and flash, set up somewhere where you have a good working distance, and start shooting. You'll get it. I promise. Why? Because if you leave the fractions for the academics to ruminate over and just pay attention to what you're seeing in your photographs, it will make sense.
The gist of it:
By definition, "an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity." Huh?
Well, for you math-minded folks, that probably makes sense. For the rest of us, what that means is that there is a way to calculate how much light fall off occurs as a subject moves farther away from a light source.
Now I'm not going to try and explain the math behind this, but the basic idea is that if a subject is one foot from the light source, the subject will receive 100 percent of the light's intensity - the square of one is one, and the inverse is 1/1, or, 100 percent. Move the subject two feet away, doubling the distance, and now they receive 50 percent of the light's intensity. Ha, fooled you. This is where the inverse square law shows up. The square of two is four, and the inverse of four is 1/4, or, 25 percent. So that one-foot difference means you lose 75 percent of the light's intensity at your subject's position.
But of course it's math, so it gets a little bit more complex than this. That first one-foot change in distance equaled a huge loss of light. But that rate of loss isn't constant. In fact, the farther you subject gets away from the light source, the less fall off you have between two distances. For example, at 9 feet from the light, the square is 81, the inverse is 1/81, and rounded to the nearest whole number you have 1 percent of the light. Move the subject to 10 feet - square is 100, inverse is 1/100, rounded to the whole number is....1 percent. The diagram below shows the rounded percentages of fall off for subjects positioned between one foot and ten feet from a light source (disregard the actual light color, I didn't calculate the proper gradient steps).
From a practical point of view, if you're photographing a subject at one foot from the light source at f/16 and he or she moves a foot back, your subject will be drastically underexposed, and to correct that, you'd use a larger aperture, say f/11. That will get you the additional light you need. Now, if that subject is at nine feet and you're at say f/4, if he or she steps back to ten feet, there's very little difference in light intensity, and your f/4 aperture can stay the same to get a correct exposure.
Imagine now photographing a group of people in two rows. If row one is positioned one foot from the light, and row two is somewhere between two and three feet from the light, there's a one to two stop difference between correct exposure for the front and back rows. The solution here would be to move the entire group back to the eight to ten foot from light source area, thereby equalizing your exposure between the rows.
Below is an example of five photographs of the same subject lit with an SB600 fired through an umbrella at 1/4 power. Shutter speed was 1/250, ISO 100, aperture at f/4.5.
So, from one foot away the side of the subject closest to the light is properly exposed. At two feet, there's a quick drop off to underexposure. At four feet, it's very underexposed. At 8 feet, you can barely make out the subject, and the same applies at 10 feet. And that's the crux of it. The difference in exposure between eight and ten feet is barely discernible, as opposed to the difference in exposure between one and two feet, which is very noticeable.
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