Today, we’re talking about mathematics and physics.
Yes, we know, you probably instinctively hovered over the back tab, ready to leave this page. Because let’s be honest, if you’ve chosen a path like filmmaking, photography, video editing, or any other creative field, chances are that part of the appeal was not having to deal with standard academia. You’d much rather work in a creative space than a formal one and that’s perfectly valid.
But here’s the thing: believe it or not, math is everywhere in filmmaking! From frame rates and shutter angles to resolution, aspect ratio, edit lengths, and file size, mathematics is rooted throughout the entire process. Unfortunately, in some way or another, you can’t completely escape it.
So today, we're exploring a fundamental lighting concept that is packed with math: the inverse square law.
Inverse square law in practice
Many variables can influence exposure and the overall presentation of a scene within cinematography and lighting. These changes can either enhance or completely undermine your intended vision.
If a scene is too dark and you open the aperture, you might introduce more depth of field than you want. You could increase the light intensity, but now the scene becomes too bright. Additional lights might help, but now they don't align with the practical lights fitted into the set. So, you bump the ISO, but that brings in digital noise.
It’s like a three-way switch puzzle: You constantly flick switches and tweak settings until you arrive at the most logical solution.
However, one important factor many new or amateur filmmakers overlook is light falloff, which doesn’t occur linearly, but rather, exponentially. Understanding this rapid light falloff is key to setting up your lighting, especially in an interior or studio environment.
Image via Lewis McGregor
But…how do we measure this, especially if lights come in all strengths and sizes? Yep, it’s the inverse square law! This law states that light intensity is inversely proportional to the square of the distance from the light source. In equation form, it looks like this:
Image via Physics Forums
Of course, we’re not here to learn equations. So, to put it simply:
- If you move the light twice the distance back, you'll get a quarter of the light.
- If you bring it into half the distance, you'll get four times the light.
Image via Hyper Physics
This doesn’t mean you need to treat every setup like a math exam by plotting numbers and solving equations mid-shoot. However, knowing that every time you double the distance from the light source the intensity is reduced by a quarter of the original amount, you can better calculate what lights and how many you’ll need, rather than bringing too much equipment or not enough.
Take a look at these helpful scenarios:
1. 10K Fresnel at 40 feet
A 10K Fresnel positioned 40 feet from the subject creates a consistent exposure across a broad area. The change in brightness within 10 feet of the subject is minimal, around 2/3 of a stop. This setup offers a very even spread of light, ideal for scenes requiring wide actor movement.
2. 1.2K HMI at 12 feet
In a second scenario, using a 1.2K HMI at 12 feet, you might get a background roughly 1 1/3 stops under the subject, enough to feel natural but still distinct. However, foreground elements that move too close to the light source will blow out by as much as three stops, so blocking must be precise.
3. 300W LED panel at 2 feet
Compare that to a 300W LED panel just 2 feet from the subject. While the subject is lit to the same exposure level, the falloff is extreme; within 10 feet behind the actor, the light level can drop by over five stops, plunging the background into near-blackness on camera. This is useful for creating mood and isolating the subject from the environment.
CGI render of 10k left. 1.2k middle. 300W right.
Each of these configurations has its strengths. A small, close light creates dramatic falloff and helps practicals and highlights stand out. A larger, distant source allows more consistent coverage over a wider area, which can help lighting logistics when actors move through the space.
Ultimately, the decision hinges on factors like the scale of the scene, the motivating source, the desired mood, and the color or distance of the background. All of these inform how best to exploit the inverse square law to serve the story visually.
If you’re still not grasping the concept entirely, it’s likely because you need to see it in action; after all, reading about how the inverse square law works will only get you so far. In the video below from photographer, John Gress, he breaks down how the law works and how it can aid your work. While Gress approaches the topic from a photography standpoint, the principle still applies to continuous lighting for film and video.
There's one aspect of this law that can be confusing at first: the idea that moving a light closer to the subject will make the background darker. That sounds somewhat paradoxical, right?
Why does the background get darker when a light is moved closer?
The idea that the background gets darker as light draws closer doesn’t seem physically accurate at first. If you turn on your iPhone torch and stand across the room, the wall on the opposite side is still likely to receive some level of illumination. And as you walk closer to that wall, you’ll notice it does get brighter.
But when it comes to larger film lights, it’s not just about brightness, it’s about distance and how the light spreads. Take something like the Aputure 300D, a hard light with a relatively narrow beam angle. If you move that light closer to a surface, yes, the light on that surface becomes brighter, but the actual spread of light becomes more focused and concentrated. You're essentially tightening the beam.
As a result, while the central hotspot becomes more intense, the surrounding area receives much less spill. That surrounding falloff, where light intensity rapidly drops, is far more noticeable.
Image via Lewis McGregor
This is because of the inverse square law: light intensity decreases proportionately to the square of the distance from the source. So, the intensity increases by four every time you halve the distance, but only within that smaller coverage area.
If you place a subject between the light and the background, it will receive most of that illumination. And because the light is now closer to the subject and further from the background, the background gets significantly less.
So, by moving the light closer, we’re not just making the subject brighter, we’re increasing the contrast between the subject and background. Conversely, if you move the light back, the intensity evens out, and the background receives more of the spill, making it brighter overall.
Conclusion
We hope that now the inverse square law doesn’t sound like something you’d hear Dr. Strange mutter in his Sanctum Sanctorum, but instead, you recognize it as a reference to the decrease in light intensity in proportion to the square of the distance from the subject.
Understanding these principles can elevate your production when you're gearing up for your next video shoot. For more filmmaking techniques and tips, be sure to check out our other resources at Film School!