The Exposure Riddle

One of the fundamental principles of photography is that pictures taken at the same shutter speed, f-stop, and ISO of the same subject, in the same light, will all have the same exposure, regardless of the focal length of the lens you use. You may need to walk up close to the subject if you’re using a wide-angle lens or walk far away if you’re using a telephoto, but the resulting images will have the same density. The change in distance from the subject will change your perspective, but it won’t change the total amount of light reaching your sensor.

The explanation for that principle seemed obvious to me until I began working on the section on lenses in my book Dusk to Dawn: A Guide to Landscape Photography at Night. As part of my research I constructed the following thought experiment and suddenly found myself quite puzzled.

Let's say you’re photographing a midtone brick wall. The lens axis is perpendicular to the wall. In other words, you’re looking straight at the wall. The lighting on the wall is completely even and completely constant. You choose a lens and position yourself so that one square foot of the wall is within your field of view. Now you choose an aperture, shutter speed, and ISO that will give you a correct exposure. In other words, the image you create of this midtone wall will be a middle tone. You snap the shutter.

Now you step back. In fact, you double your distance from the wall. That means that the vertical and horizontal dimensions of the area within your viewfinder also double. That, in turn, means the area within your field of view increases by a factor of four. You now have four square feet of wall within your field of view instead of one. Since the wall is evenly lit, the lighting is constant, and the area within your viewfinder is four times as great as before, it would seem logical that four times as much light would reach your lens. If you use the same settings for shutter speed, aperture, and ISO, it would seem logical that you would overexpose the second image by two stops. Each full stop represents a doubling or halving of the amount of light reaching the sensor. Yet the two exposures—the total amount of light reaching the sensor—are the same for both images when you use the same shutter speed, aperture, and ISO. How can this be?

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