The Inverse Square Law for Photographers. A Visual Approach to the Inverse-Square Law of Light

 

The inverse square law is one of those phrases that strikes fear into the minds of new and even experienced photographers. Why? Because we are talking about physics, equations… You know…math! But don’t worry. I am going do my best to simplify this inverse-square law stuff for you.

Watch the VIDEO…

There are tons of explanations out there about the inverse square law, and they all start out with the MATH – even though most of them admit that you really don’t need to know the math. If you’ve watched or read any of my stuff, you’ve probably heard me talking about not using four letter words like AUTO, RULE, POSE, and FILM. And, well,  MATH is a four letter word. So DON’T use it! For all you numbers geeks – if you want to know the equation and the exact math behind the inverse-square law, I don’t want to waste your time; you’re not going to find it here. There is this thing called Google, I suggest you go check it out.  For those of you that want to gain a practical understanding of the inverse square law and WHY it is such a big deal, pay close attention…

There are two pieces of physics that every photographer MUST learn if they want to be able to consistently create great photos. One is Depth of field (which I’ll get into at a later time) and the other is the inverse-square law.

The inverse square law is about how fast light falls off and how far it spreads as the distance from the light source increases.

Light intensity or brightness drops much faster closer to the source than it does further away from the source. That also means that the closer your subject is to your light source, the harsher the shadows and the quicker the light will dissipate.  The further your subject is from the light source the dimmer the light will be; the shadows will be softer and the light will spread over a larger area.

Example 1: The Eggs

eggs with faces on them lined up in six inch increments to demonstrate inverse square law.

Take a look at my lineup of eggs… The eggs are set 6 inches apart and at f/22 the first egg is properly exposed. Pay close attention because this is where most people start to misunderstand the inverse-square law. In order to get the proper exposure for the second egg – we need to shoot at f/11. That’s not one stop, but two stops difference.  You see, each time you double the distance of the subject from the flash, the light falls off by four times, not two times.

You maybe scratching your head as you read this, but don’t give up yet! The inverse-square law really is your friend. It is a very powerful tool… as long as you understand how it works.

Still confused? Let’s look at an even easier but more useful example…

Example 2: The Portrait Subject

digital rendering of portrait subject with light at 3 feet

Here you see a portrait subject seated 3 feet in front of a neutral gray background. The light is a medium sized softbox placed three feet in front of the subject and my aperture is f/16. In the finished image you see a darker gray background and well-defined shadows on her face.  You also see large catchlights on the camera left side of the eyes.  Notice also that the catchlights are in the upper half of the eyes, where they should be. To achieve this I have the softbox placed with 2/3rds of it above the face and only one third below, since I still want the light to have a natural top-down effect.

So let’s move that light back to 6 feet, which is double the distance of the 3 feet example.

digital rendering of portrait subject with light at 6 feet

Now my aperture changes to f/8. I have doubled the distance of the subject to the light and as a result I have just 1/4 of the amount of light- which is a two full stop difference. You should also note that the background appears a little lighter and the shadows are softer and the catchlights are smaller.  Remember this is the same medium-sized softbox with the same power settings on the flash – just at double the distance.

Let’s double it again. This time I am going to move that softbox back to 12 feet.  

digital rendering of portrait subject with light at 12 feet

Remember – I started at 3 feet – doubled it to 6 and now I have doubled again to 12. Now my aperture changes to f/4 because I have only 1/6th of the light that I started with. You can see that the shadows are even softer yet. The gray background is even lighter and the catchlights are even smaller.

Let’s compare all three.

All three images side by side

You can see as the light moves further from the subject – the shadows soften, the background gets brighter and the catchlights get smaller. The flash is set at the same power for all three shots and the softbox is set at exactly the same height for all three.

Remember this tip: Light Close for sharper shadows, bigger catchlights and darker backgrounds. Light Far for softer shadows, smaller catchlights and brighter backgrounds.

That’s just one way that the inverse-square law impacts your lighting.  Let’s look at another scenario…

Example 3: The Two Models

two models, one 3 feet and one 4.5 feet from light to demonstrate Inverse-square law

In this setting I have two models that are 3 feet and 4.5 feet from the light source. You can see the model on the left is much brighter than the model on the right.

If I move the two models to 6 feet and 7.5 feet you can tell the model on the left is still a bit brighter than the one on the right but definitely not by as much in the first example.

two models, one 6 feet and one 7.5 feet from light to demonstrate Inverse-square law

In this version if I move them to 12 feet and 13.5 feet from the light source you can see that they are virtually the same brightness.

two models, one 12 feet and one 13.5 feet from light to demonstrate Inverse-square law

Let’s look at the close-ups. The first version – close to the light source – the model on the left is much brighter. The middle distance the models are closer in brightness. And in the final frame the models are virtually the same brightness.

comparing all three finished images

You can see that each time I double the distance I lose two full stops of light. I promise you – it is more important to remember visually what you see happening here than it is to remember how many stops of light you lose at what distance. That’s why we have light meters…so that you don’t have to do the math!

When photographing two or more people, back your lights up to keep your subjects evenly lit.

Common Inverse Square law mistakes 

Now that you have seen three different scenarios and how the inverse-square law impacted them… let’s look at a very common mistake that new and young photographers make while they are learning the ins and outs of lighting.

Unfortunately I see this mistake frequently in images posted in my Facebook group and that is a photographer putting their light source or modifier too close to their subject. When you do that you wind up with a situation where the top of the subject’s face is brighter than the bottom, or, one like below, where the subject’s hand is brighter than her face, which causes the hand to be a distraction.

Light too close to subject and lighting up her hand

Since we understand how the inverse square law works now, we know that if we back up the softbox and raise it slightly – we get the same skin tone and brightness on the subject’s hand and face, as in the example below. 

softbox backed up, more even light

I find photographers making a similar mistakes with models standing too close to a light source. It is fine if their arms and hands are at their sides, but if they move part of their body closer to the light, you wind up with a very bright hand.  If we simply back up the light source we can even out the light so that the hand and the face are of equal brightness. Check out the video at the top of the page (or click here) for more examples. 

Are you getting the hang of this yet?  Please notice that I haven’t made you listen to all that M A T H stuff.  The reality is that, while there is nothing wrong with knowing all the physics behind the inverse square law, what is more important is understanding how it works and practicing so that you learn to recognize these challenges and how to use the inverse-square law to overcome them.

The Science of Spreading Light

In addition to the intensity of the light diminishing rapidly, the light spreads as it gets further from the source.  You can see in the diagram below that at a distance of 3 feet, my light source is covering 9 square feet and my subject is properly exposed.  

Light spreading diagram

Now we learned with the eggs in example one that if we double the distance to 6 feet we will have one quarter or 25% of the light intensity – but look at what happens to the spread. Now the light covers four times the area, or 36 square feet. If we move three more feet to 9 feet we now have just 11.11% of the light intensity but we cover an area that is 81 square feet.

Take a look at this group shot that is lit with two shoot-through umbrellas and speedlights – one on either side and fairly close to the group.  

group shot with seven people, four sitting three standing, lit with two speedlights really close to group; uneven light, harsh shadows on backdrop

The lighting on the group is not even as the people on the outsides are somewhat brighter than the people in the middle.  If we back the lights up now the group is evenly lit from side to side and front to back and the crazy shadows on the wall are almost completely eliminated.

back up lights on group; much more even lighting than before

So the simple math is that if you need to cover a bigger area – back that light up.

Modifiers and the Inverse-Square Law

Now I know that some of you are thinking, “What about the modifiers?”  The modifier doesn’t really impact the inverse square law– it impacts the shape and softness or even the intensity of the light. The light coming out of a softbox will still spread as it gets further from the source. This applies to beauty dishes, umbrellas, octoboxes, parabolic reflectors and even snoots.

Backgrounds and the Inverse Square Law

If you have been paying close attention you should have noticed that you can also use the inverse-square law to change the tone and brightness of your background.

Let’s look at this setup below with a beauty dish and a reflector. With my subject 3 feet in front of a gray background and the dish about 2 feet in front of my subject, we get this medium to dark gray rendition of the background.

subject in front of gray background with beauty dish above and reflector below

If we double that distance the background gets even darker yet. And if we move the subject and the light even further from the background we get a nearly black background that still provides a little separation. All of this with one light and one reflector.

same shot at three different distances from background, backdrop color changes with distance

Needless to say I could go on for hours with variations.  Just understand that if you want to be able to consistently produce well-lit images using studio strobes or speedlights or LED lights – you can’t ignore the inverse square law. The sooner you embrace it and work to understand it, the better your lighting will be.

Your Inverse Square Law Cheat Sheet:

  • Light close for sharper shadows, bigger catchlights and darker backgrounds.  Light far for softer shadows, smaller catchlights and brighter backgrounds.
  • If you are photographing two more people, back your lights up to keep your subjects evenly lit.
  • If you need to cover a bigger area, back that light up.

So there you have it. The Inverse Square Law. Just so you know what you missed by not talking about the MATH…. here is the equation:

intensity of light is equal to the inverse of distance squared

Ok – now that you’ve seen – forget it.  Go set up some lights and practice!

So until next time, gang, go pick up that camera and shoot something because your BEST shot is your NEXT shot. So keep learning, keep thinking, and keep shooting. Adios!

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