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The Inverse Square Law of Light: The Science Behind Perfect Lighting

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Light is one of the essential components of photography. How a person manipulates light through the intelligent use of aperture size and shutter speed, affects the quality of the photos taken immensely. Therefore, if you are a professional photographer or even an amateur one, who wishes to take stunning photos under different lighting condition, then you should have a thorough knowledge about the properties of light. One such important law of light for photographers is called the “inverse square law of light”.

The inverse square law of light is something that helps you better understand how to use the light sources around your subject. Want that perfect photo? Read up all about this concept.

The Basics

What inverse square law of photography is and how it affects the quality of the picture taken is one of the fundamental concepts of photography. Understanding this concept will allow you to take photographs even in adverse light condition with amazing results. However, before learning about this law, you first have to familiarise yourself with the working of a camera aperture and how it affects the entry of light inside the camera.

Aperture

inverse square law of light aperture
Photography 101: Aperture (Source)

Aperture is the opening of the camera that allows the light to enter inside the camera and fall on the sensor (on earlier cameras it used to fall in the camera roll) and create an image of the reflected object on the sensor. The light that an Aperture allows to enter inside the camera is calculated through F-Stops. These F-Stops follows the inverse square law of light.

F-Stops

F-stops are a set of numbers in your camera that tells you how much light is entering through the aperture inside the camera. And, as the aperture of a camera is adjustable, you can increase or decrease its size to regulate how much light enters the camera. The F-stop is a scale integrated into the settings of your camera that tells you how much light you can get inside your camera to take that perfect shot. As you move up the scale, every F-Stop number doubles the amount of light that is entering the camera.

inverse square law of light f stops
Let the Light In (Source)

So, if you are shooting in a low light condition, then you need to let in more light and when you are shooting in broad daylight you have to go down the F-Stop scale to minimise the exposure. As you move up and down the F-Stop, the diameter of the Aperture increases and reduces, allowing you to get the perfect condition and take the most realistic looking shot. While aperture plays a big part in regulating the amount of light that enters the camera, it is not the only element that affects the exposure.

The lens, shutter speed, and ISO also play a vital part in it. The focal length of the lens in conjunction with the Aperture allows a certain amount of light to enter inside the camera.

The Connection between Flash Head, Output, ISO and Aperture

When you want to take photographs in low light conditions, you need to have a thorough understanding of the relationship between the flash of your camera, how much light it is producing, the ISO figure, and the opening of the aperture. As the flash light literally dumps all the light in a fraction of a second, the role of shutter speed is not that important while taking close photos with the help of flash light. On the other hand, ISO setting is adjusted to take good quality photos in different light condition.

For example, if you are taking photos of a bright sunlight condition, then keeping the ISO low will help you take a high-quality picture without any noise. However, if you keep the ISO level low in a low light condition, then it will be very difficult to take quality pictures in hand held position of the camera. All the photos will be blurred. To rectify, this problem, we increase the ISO reading in the camera settings.

inverse square law of light iso
Everything is Linked (Source)

To put it in simple language, flash exposure is controlled by the aperture and when you increase the ISO, it affects the amount of light from the natural flash source as well as ambient exposure. Therefore, if you are shooting in a low light condition where the subject is fully exposed, with a flash and want a more ambient background, lower the shutter speed without adversely affecting the mixture of different temperature.

If the condition is reversed where the background is okay but the subject is not fully exposed, then change the aperture settings. However, when you are using a flash and the condition is such that both the subject and the background appear too dark or bright, then you should adjust your ISO settings to get that perfect shot.

The Inverse Square Law of Light

The subject that relates to photography lights is very interesting and tells you how to master the natural light to shoot a picture. The importance of light in photography cannot be overemphasized, as it allows you to improve the tone of the subject and add to the atmosphere of the picture that you wish to click.

Light and its effect on the photo include the intensity of the light, positioning of the light source, and the use of diffusers in front of the light source.

Let's understand these terms one by one and find out their effect on taking good quality photos.

  • The intensity of the light is an important factor in clicking great pictures. If the natural light source is not enough to expose the subject and its background, then we use artificial light sources.
  • The positioning of light allows you to add dramatic features to your photo. The light source can come from the back of the camera, from the side of the subject or even from the back of the subject.
  • Adding a diffuser in front of the light source reduces the glare allowing you to take softer and more natural looking photos.
diffuser inverse square law of light
'Diffusing' the Situation (Source)

The importance of light in photography is well established and when we talk about the light, then one particular law of it plays an important part in taking photography, which is the inverse square law of the light formula.

To understand the inverse square law of photography, you have to realise that light does not fall linearly on a subject. If you double the distance between the source of light and the subject the light falls with four times less intensity in the subject. In another words, the further you take the light source away from the subject, the amount of light that falls does not diminish proportionally but by the square of the distance between the light source and the object. Also, the light on the subject falls as the distance increases.

This is why this law is called the “inverse square law of light”. The word “inverse” denotes that the light on the subject falls as the distance increases and the word “square” tells you that it falls by the square of the distance.

Formula for the Inverse Square Law of Light

The inverse square law of light formula shows that

P = 1/Distance2

(Where P denotes intensity or power of light.)

As the power leaves the source, it begins to ‘fall off’, so we need a starting point for measurement. This starting point is called “full power”. Here the formula works for any unit of measurement be it cm, inch, or feet. Because in an inverse power law, the full power is relative, as at any one unit of measurement the result will always be the same- full power. To prove it mathematically,

P = 1/Distance2

If we take distance as 1 unit (the unit could be in feet, meters, cm etc) and put it in this formula, we get the following result:

P = 112

P = 11

P = 1, which means full power.

formula for inverse square law of light
How Light Works (Source)

Here the unit of the measurement does not count. This law is applicable to any unit of measurement of length as long as it is consistent.

As the distance increases, the power of the light diminishes by the inverse square of the distance. Like if we move the distance by 2 and 3 feet respectively, then according to the formula:

Distance= 2unit

P = 1/Distance2

P = 122

P = 14

Distance= 3 unit

P = 1/Distance2

P = 132

P = 19

As we move down the scale, we realise that the further we move from the source of light, the power of the light falls off quickly. However, as we go farther away from the light source, the rate at which the light falls of is reduced a great deal. In other words, the luminosity of the light diminishes at a slower pace when we move farther away from the light sources. This law gives us an idea of how the light will react when it moves away from the source, which allows us to manipulate it to give some dramatic effect to out pictures.

If we look at the inverse square law of light calculator, we find that as we increase the distance of the object from the light sources successively to one unit, 2 unit, 3 unit and so on, the F stop does not increase uniformly. When we move from 1 unit to the 2 unit we lose 2 full stop of power, when we go from 2 unit to three, we lose one full stop of power, and as we go further, we find that as the distance increases like 4 unit to 5 unit, 5 to 6 unit, 6 to 7 unit and 7 to 8 unit, we only lose ½ stop of power. As the distance of the object increases further from the light source like 8 to 9 unit and so on, the fall in stop power gets reduced to ¼.

Inverse Square Law of Light: The Practical Application

This law has a wide use in the field of photography and we can use it to put more dramatic atmosphere in the picture. Like if you want to focus on the subject itself and would like the background to be darker, then putting the object closer to the full power will give us that result. In such a photo, not only will the background appear darker but there will also be sharp shadows on that part of the face which is not in line with the full power of the light (this may happen if the light source is placed at the side of the object).

However, if we wish to keep the shadow effect on the face but at the same time get a better exposure to the background, then putting the object a little distance away from the light sources will do the trick.

inverse square law of light practical
The Game of Light (source)

In real life photography, if we see that the object is very close to the source of light, then we need to adjust to its smallest diameter like F 16 so that all the extra light surrounding the object is cut off. However, if the object is far away from the light source, then we must open the aperture all the way so that more light is captured to get better exposure of the object. This rule also affects the how the exposure of light happens while clicking the image of a single object or a group photo.

If it is a single person is sitting very near the light source, then if there is any movement during the photo shoot by the object towards or away from the light source, then it can lead to over or under exposure. If you are taking a group photo and the group is very near the light source, then the one who is closest to the light source will be over exposed and the one at the further end of the light source will be under exposed. To rectify this situation, the subjects are placed further away from the light source to get uniform exposure.

While the law itself is pretty easy, it is only through constant practice, that you will be able to master this rule and take amazing photos.

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