The Inverse Square Law and Bounce Flash

The Inverse Square Law: These four words are bound to make people uncomfortable. It all sounds like math, and it is. But it is the principle that is definitely worth knowing, particularly when applied to indoor lighting. Simply put, the Law states that if you double the distance, the intensity of the light decreases by a factor equal to the square of the distance, inverted, or more simply, decreased by a factor of four.


It was my intent that this entry would be a discourse on the mathematics involved, but thought the better of it. Instead, here's a sample of a photo that only works because the Inverse Square Law (ISL) is applied in a difficult environment.

The "Honoring Our History" Traveling World War I Exhibition was in Redwood City on Friday, February 10, from 9 a.m. to 4 p.m.  It was housed in a trailer to facilitate setup and takedown, and to insure that the exhibits were ready for viewing wherever the trailer stopped. I was in a bit of a hurry to make the photo and return to my office, so I didn't have time to examine the trailer. It suffices to say that there was a lot of exhibit stuffed into a small, mobile space.

Notice the black ceilings and walls. This was to minimize glare from the glass display cases, but it makes for a very dark shooting environment. When I saw this, I was momentarily stumped, since I couldn't use ceiling bounce. However, I was standing in front of a panel display, so I aimed the flash to my rear and the let the light bounce off the panel and onto the two viewers. This isn't artful light. It simply does the job, allowing for even illumination from the foreground through the background. The speed light lost nearly all of it's power by the time it got to the uniform on display in the back. The exposure (F 5.6, ISO 800, 1/60, Flash WB), allowed for some detail in the back. Due to the crowded conditions, I felt it unwise to attempt to set up a gelled remote to brighten up the display.

Direct Flash: Direct flash will result in a greater difference in illumination levels between the subject and the background. Now For The Math: Let's re-examine the Inverse Square Law. Let's  assume that a photographer must make a photograph using a camera with an on-camera flash. The subject is five feet from a camera and five feet in front of a blank wall.  This means:

• If 5' is the distance from the flash to the subject, and
• If 10' is the distance from the flash to the blank wall (5' from the flash to the subject + 5' from the subject to the wall),
• Then the light that hits the blank wall will be 1/4 as much as the light hitting the subject.

Follow that? You see, the distance from the light to the blank wall is twice the distance from the light to the subject. That 1/4 factor equals 2 stops of underexposure. That's noticeably dark.

Bounce Flash: Now when I bounced off the display behind me, the distances change. Assuming that I am standing 5' in front of the display, it means:

• If 15' is the distance from the flash to the subject (5' from the flash to the display + 5' back to the photographer + 5 feet to the subject, and
• If 20' is the distance from the light to the background (the previous 15' + 5' from the subject to the subject),
• Then the light that hits the blank wall is slightly less than 1/2 as much as the light hitting the subject.

Huh? Here's the magic number. If I experience a 2 f-stop drop when the distance is doubled, what is the distance factor to get a 1 f-stop drop? It turns out that the factor is about 1.4, which is the square root of 2 rounded up slightly.  Trust me on this one. (I once went through the mathematical proof to derive this value, but the students, for the most part, went blank). Now if I multiply the 15' flash to subject distance, the 1-stop reduction distance is 21' (1.5 X 15).

Now you don't need to know the math. But you can take advantage of the even front to back illumination when you bounce your flash. This is why bounce gives such even light, as it not only produces a very broad light source, but evens the exposure because the increased distance the light must travel.

So bounce with my blessing!