The Inverse-Square Law - There is just no escaping how light decays!

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Google the inverse-square law (as it relates to photography) and you will almost certainly be flooded with articles that use the concept to explain how to position a model. The theory goes that if a model stands close to a light source, a large flash perhaps, then the result will be a high-contrast image, one with bright highlights and deep shadows. Place the model some distance away from the flash, though, and the lighting will appear altogether softer, with a more even balance of highlights and shadows.

The phenomenon exists because light has a very distinct way of fading from, well, ‘light’ to dark. In other words, there is a specific formula that dictates how the intensity of light changes as it travels away from its source and that formula is known as an inverse square.

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If, like me, you were geek enough to chart the change in light intensity over distance, the results from the above equation will look something like this:


The important thing to take away from this graph is that the intensity of the light decays rather quickly as it first moves away from its source, but that the rate of decline slows to a mere dawdle as it gets more distant.

Think, once again, in terms of a model standing close to a flash. The model is standing in the steepest part of the curve, and the steepness means that the portion of their body that is closest to the bulb will be appreciably brighter than the portion that is furthest away. To reach the outermost parts of the subject's form, light must travel further, all the while rapidly losing its power. Compare this scenario to a more distant model, one far enough away to be in the flatter part of the curve. Here, the closest and furthest portions of the body will be more evenly lit as the light intensity is dropping comparatively slowly while it travels across the model.

Whether you are taking photos of a model in a studio or designing the inner workings of a lens, there is just no escaping the manner in which light chooses to decay.

So, What does all this talk of models and flashes have to do with landscapes photography? I hear you ask. Well, nothing, but it does tell you a lot about why your lenses work as they do. For example, have you ever wondered why aperture values are stated as a function of focal length, for instance, f/2.8 or f/5.6?

The reason is that as light travels down the length of the lens barrel, its intensity decays precisely as the inverse-square law says it should. From the camera sensor's perspective, the first optical element of a lens is the light source, akin to the flash from earlier. The shorter the focal length, the closer the sensor is to the light sources and, consequently, the higher its intensity. Increase the focal length, and the intensity of the light hitting the sensor decays obeying the inverse square.

Thus, to give photographers a fighting chance of being able to expose correctly at different focal lengths, a method was devised to ensure that light intensity at one focal length could be accurately replicated at another, essentially cancelling out the effects of the inverse-square law which, inside your lens, are less the desirable. The solution was to tie the size of the aperture to the focal length; the longer the focal length, the bigger the physical size of the hole.

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To illustrate how this works, consider the physical diameter of an f/4 aperture. At a focal length of 16 mm, the hole in the front of your lens has a diameter of 4 mm (16 mm ÷ 4) , while at a focal length of 80 mm, the aperture hole is 20 mm across (80 mm ÷ 4) . The larger opening at 80 mm allows more light to enter the barrel and, if the lens manufacturer has done the maths right, this should see the intensity of the light striking the sensor being identical for both situations.

In fairness, there are other characteristics of light, optics and, indeed, mechanics that influence the relationship between aperture and focal length for a given lens, but the inverse-square law is undoubtedly the primary contributor. The inverse square is a fundamental property of light in general, with a sphere of influence that far exceeds the boundaries of a simple camera. As general as the concept is, though, the effect of the law remains an intrinsic part of photography, the consequence of which impacts upon every part of the discipline. Whether you are taking photos of a model in a studio or designing the inner workings of a lens, there is just no escaping the manner in which light chooses to decay.