###### Definition

The Inverse Square Law can be summed up as follows:

The intensity of light radiating from a point source is inversely proportional

to the square of the distance from the source; so, an object (of the same size) twice as far away receives only one-quarter the light in the same time period.

Intensity of Light

The intensity of light depends on two main criteria: The distance between the light source and the subject and the background, and the subject + background to the light source. Confused!

Let me explain.

The closer the light source is to the subject, the greater the intensity of light and illumination. Moving the light source closer or farther away from the subject alters the level of light falling on the subject. And how fast light falls off and how far it spreads as the distance from the light source increases.

If you halve the distance between the subject and a point light source such as a Speedlite/flash unit, you will increase by four times the amount of light reaching the subject, a term which is referred to as the Inverse-square law. Halving the distance between the light source and the subject quadruples the illumination, and doubling it reduces the illumination one quarter. This, in turn, gives us greater control over exposure settings since more light gives the photographer a greater choice of lens aperture and shutter speed combination.

Still confused. Let's break this down into easy to understand steps.

Example:

To fully understand the basics. Setup a Speedlite/flash along a white wall. Mark off the wall every meter 1 - 8.

Put your Speedlite/flash on maximum full power 1/1 record this as 1 at the 1-meter marker. Use a light meter to measure the light intensity at each marker to obtain the aperture f/ number.  We know from a previous lesson: The Aperture controls the Flash exposure and the Shutter speed controls the ambient exposure. The only limitation being "Sync speed". Which I will go into more detail on this in the advanced course

Leave your Speedlite/flash on this full power setting as you continue to record the power setting 2 - 8 at each meter marker, exactly like the image above. So you will fire off the Speedlite/flash 8 times.

Once the Speedlite/flash is fired at full power 1/1. Your light meter will record an Aperture meter reading of f/22 at 1 meter. At 2 meters, your light meter will record a light meter reading of f/11 decreasing the quantity of light by a factor 4 (2 f-stops). The intensity of the light source has diminished rapidly from 100% at the 1-meter marker to 25% at the 2-meter marker. A drastic decrease of 75%.

"If you double the distance from your subject, you quarter the power from your light source."

###### Inverse Square Law

0             1                2              3               4               5              6               7             8             9             10

0           1/1            1/4           1/9           1/16         1/25        1/36          1/49      1/64       1/81       1/100

100%          25%        11,11%      6,25%       4%         2,78        2,04%    1,56%     1,23%       1 %

###### Light fall off

f/22            f/16          f/11           f/8%        f/5.6        f/4           f/2.8        f/2         f/1.4 %     f/1.2

In the image above we can see that there is a 75% drop in light from meter 1 to meter 2.

This indicates a drastic difference of 75% of light fall off.

So by placing the model closer to the light, she will have greater shadows, higher contrast (a higher degree of light differentiation between the bright and dark areas).

In the image above we can see that there is only a 5% drop in light from meter 4 to meter 10.

This indicates a gradual difference in the fall off of light. It is way less at 5%.

Placing the light further away from the model will cause the light to be diffused, softer and have less deep shadows.

Image 1: The light source placed at 1 meter will create a much shorter fall off of light. This isn't ideal if you are photographing a group of people as the 2nd, 3rd and 4th row will be drastically underexposed. We are losing 4 stops of light between the 1st and 4th models. Not ideal for taking any head to toe images. As the model from waist height will be going into darkness.

Image 2: The light source is placed at 2 meters and we can already see a slight improvement to the faces of models 1, 2. Moving the light back 2 meters has caused the light to only lose 2 1/3 stops of light.

Image 3: The light source in this image is pulled back even further to 4 meters. Now we can see that models 1, 2, 3, and 4 are more evenly lit. It isn't 100% perfect, but we are getting there. By moving the light back we can also see that the background is starting to get evenly lit. At 4 meters, we are only losing 1 1/3 stops of light.

Image 4:   The light source in this image is pulled back to 8 meters. We able to verify that the models are evenly lit, and our background is evenly lit, as well. At this distance, we are able to capture perfect head to toe images and backgrounds. This lighting setup is ideal for groups as the light will be evenly distributed, from the front row way into the back row. in this example we are only losing 2/3 stops of light.

Image 1: The model is placed 1 meter from the light source and she is exactly 2 meters from the background. So the closer the light source the great will be the fall off of light. Thus creating greater shadows and because she is fairly close to the background, deeper darker shadows, or a complete darkened background. The photographer is losing 3 stops of light f/22 to f/8. Which indicates a drastic fall in light. She is not evenly lit. You would not use this lighting setup for a full portrait image. As the fall off of light is way too drastic.

Image 2: The model is placed 2 meters from the light and is standing in the exact same position as before at 2 meters from the background. In this situation as the light source is being pulled back, to lessen the intensity of light on the model. We notice more light falling on the background and the model. The shadows on the model are beginning to get softer and the background shadow is becoming more feathered and softer as well. Moving the light back 1 more meter to 2 meters has given the photographer more light to work with and he only looses 2 stops of light. The light is now hitting the model's knees. Ideal for some types of portraits.

Image 3: The model in this image is positioned in the exact same position at 2 meters from the background. The light source is pulled back to 4 meters. The model is evenly lit and we can now capture a full head to toe portrait image.  The model and her background are evenly lit. The photographer is only losing 1 stop of light, f/5.6 to f/4.

All images are captured with the same light power setting.

###### Exposure rules

If you want a darker background, you would place your model close to the light and away from the background. The fall off of light will be more drastic. The background will appear darker.

It's important to point out, that this lighting setup isn't ideal for head to toe images. As the lower part of the models, body will be in less light and will appear darker.

If you place the model further away from the light source, but nearer the background. We know from the above explanation that there will less of a percentage fall off of the light intensity and the model will be evenly lit. Ideal for trying to capture full head to toe images that are evenly lit against an evenly lit background as well.

Placing a group of three people nearest to the light will cause the light fall-off to be more drastic. As all three models are far away from the studio wall. The background will appear fairly dark. The model right next to the light source will be correctly exposed, the 2nd model will begin o show signs of starting to be underexposed and finally, the 3rd model will be completely underexposed and may blend into the dark background as well.

Do not use this setup lighting method if you are trying to capture a group of models, and require all three to have perfect exposure.

If the light source is further away and the group of three models is near the studio wall. The fall-off will be less intense. It will be ideal for lighting every model and the background evenly. The exposure of each model standing next to each other will be similar and more consistent.

If you need to drop the light off the background to deliberately make it darker, place your model away from the background and close to the light. The light will fall off fairly quickly and your background will appear very dark. This is ideal lighting if you want to create moody and artistic nude images. As the drop off of light will allow the photographer to create stunning fine art nude images.

To achieve fairly even exposure for both the model and the background. Move the model away from the light source and closer to the background. The fall off of light will be less drastic. The light will be more diffused and softer. Lighting the model and wall evenly. Ideal for lighting a nude in her surroundings. When the surroundings are just as important as the model.

Okay! So let's recap what we have learned in this tutorial.

1) If we place a model away from a background and closer to the light source. The intensity of the light source diminishes more rapidly.

2) Light spreads more evenly the further a model is away from the light source.

3) Light intensity/brightness drops off much faster - closer to the source than it does further away from the source.

4) Put the light close to your model to create deeper shadows, bigger catchlights in the model's eyes and a darker background (model needs to be some distance away from the background)

5) Put the light far away from the model against a background, to create softer shadows, smaller catchlights, and a lighter background.

6) If you are photographing two or more people,  pull your light source back to evenly light them and have a consistent exposure.

7) If you need to eliminate shadows you will need to move the light source away from the model.

8) If you want to create fine art images with deep shadows, you will need to move the light source closer to the subject.

9) Light further away from your model, more consistent exposure.

10) Light closer to your model, a higher degree of differences in exposure between the model and the background depending if she is near or away from the background.

11) If the light is closer to our model we will have shorter intense illumination. But if the models is far away from the background, the background will be darker.

12) If the light is far away from the model, but the model is close to the background. There will be a wider area of illumination.

13) To darken the background you would need to put the model closer to the light source and away from the background.

14) If we place a model further away from the light source but near the background. there will be less of a percentage difference in light fall off. And the model will be evenly lit.

15) Exposure 1: To achieve the perfect lighting for a group of models in a studio setting, place the light far away from them so that it evenly lights the models and background.

16)  To achieve high contrast images, to create fine art nudes with lots of depth and atmosphere. Move the light source closer to your model and have the model move away from the background.

17) To isolate a group of models have them stand away from the light source and background so that they are evenly lit, but the background falls off fairly quickly.

18) To include a group of models with their background, place the group of models next to their background, and move the light source far away. To widen the illumination.

Conclusion

It is important to understand the fundamentals of the Inverse-square law, as it allows a photographer to have full control of how much light will fall onto a model and the background. It gives us full control to achieve perfect exposure for a model, a group, or subject matter against a background at a specific distance.

The core principals of the Inverse-square Law teach us that the power setting on our flash and the fall-off of light that occurs as a result of these settings. Exposure is directly influenced by the distance we place our model to the light source and the background.

As we can see from the above explanation. There are two important lighting controls we need to consider before capturing our first image. The first being the actual lighting power and camera settings.

In order to capture a perfect image, these two need to work in conjunction with one another to achieve perfect exposure. To keep this tutorial fairly simple to understand. I have deliberately left out the specific "Shutter speed, ISO, Aperture" requirements, required to achieve perfect exposure. I've touched on this in the basic explanation above. But as you can see, there is no mention of ISO, Shutter speed and Aperture in full, and how these three components work in conjunction with one another and the flash power settings, the light source position, and the distance from the model and the background.

I have kept the explanation brief and straight to the point, so that you are able to grasp the fundamentals of how the light behaves according to a particular power setting, its position "distance" to a model and the background, and a given aperture.

In the advanced Speedlite/flash course. I will be going into more detail about how the Inverse-square law is used with the ISO, Shutter speed and Aperture, and how they are influenced by the power setting we select on the Speedlite/flash and how we can manually control the ISO, Shutter speed and Aperture to achieve perfect exposure, based on the principals of the Inverse-square law.