# UNDERSTANDING THE LAW OF REVERSE SQUARES FOR PHOTOGRAPHERS

The laws of photography sometimes seem too complicated to understand and it gives the wrong impression that a mere mortal can not be thought of and not taken into account in his shooting. Understanding the rules allows you to think freely and makes it possible to realize the flight of your own imagination. Understanding the laws of light painting is better with the masters of their craft.

Johannes Downer is the founder and CEO of Elixxier, which developed the set.a.light 3D program, which allows photographers to virtually simulate lighting schemes and plan the technical details of photo shoots. We want to familiarize you with the material in which it gives clear explanations of the Law of Inverse Squares, which is so necessary for every photographer and photographers shooting in the studio, in particular.

“It is not difficult to write down the formula of the Law of Inverse Squares, only basic mathematical knowledge is required. But the physics of the process behind it is much more complicated. Therefore, we will consider the law only by examples and from the point of view of photography. We will talk about the light falling on the film or image sensor of a digital camera, and the lighting of the subject. The law of inverse squares is extremely useful and applicable when shooting with flash.

First, let’s look at how the diaphragm is connected with the Law of Inverse Squares, and how this relationship affects the decrease in light intensity. To make it clearer, let’s start with the diaphragm.

By covering the aperture, you reduce the amount of light that passes through the lens. Changing the aperture for each subsequent stage reduces the diameter of the aperture by 1 / √2. In simple terms, the relative aperture and amount of light decreases exactly by half.

This technical breakdown allows the photographer to adjust aperture and shutter speed to suit lighting conditions. Since each next aperture value (it is also the aperture stage) is obtained by multiplying the previous value by the square root of 2 (or 1.414) and the value is rounded to 1.4, it turns out, for example, that the next value after the f / 4 aperture is f /5.6 (4 times 1.4).

Accordingly, the well-known f-number scale is as follows: f / 1 f / 1.4 f / 2 f / 2.8 f / 4 f / 5.6 f / 8 f / 11 f / 16 f / 22 f / 32

Understandable Inverse Square Law for Photographers

In rare cases, such as macro lenses, the scale continues to f / 45. This is necessary in order to achieve an acceptable depth of sharply depicted space, because macro lenses are shot from a very close distance to the object.

The law of inverse squares in lighting

The law of inverse squares helps to achieve perfect lighting in each specific situation. It works simply: if you double the distance from the object to the light source, the source will illuminate a four times larger area.

In other words, in order to calculate the increase in lighting area, you need to square the distance. At the same time, an increase in area leads to a decrease in the intensity of illumination inversely proportional to the square of the distance, because the same amount of light will spread over a large surface.

Technically, the Law of Inverse Squares reads as follows: “The energy (in our case, light intensity) at point A (location of the subject) is reduced inversely with the square of the distance from point A to the energy source (in our case, for example, to a studio flash).” Understandable Inverse Square Law for Photographers

Area and intensity: details about the Law of Reverse Squares

Understandable Inverse Square Law for Photographers

For example, the light intensity increases by 4 times with a decrease in the distance from the light source to the subject by half. In turn, if you double the distance, the intensity will decrease to a quarter of the original. Using the same algorithm, one can calculate exact pairs of values with a further increase in distance (distance is 3 times, intensity is 1/9; distance is 4 times, intensity is 1/16).

In general, the Law of Inverse Squares indicates a disproportionate decrease in the intensity of illumination with increasing distance between the light source and the object. It helps to understand the relationship between light and lighting and the distance to the object and its brightness. It is clear about the Law of inverse squares for photographers

Practical application

According to the Law of Inverse Squares, the illumination intensity drops sharply with an initial increase in the distance from the light source to the object. A further increase in distance leads to a decrease in intensity to a lesser extent. For example, if we increase the distance from the flash to the subject from 1 meter to two, then we will lose 75% of the light intensity at the subject. But with an increase in distance from 4 to 10 meters, only 5 percent is lost.

It follows that the light intensity near the source has the highest values, and only crumbs remain at a distance.