The Inverse Square Law - Have I been lying all these years?

Also in this issue:

• Kenya Trip Report
• Next Time in CameraCraft Magazine
• Upcoming Seminars
• In the Pipeline

The Inverse Square Law

Imagine you brought a gun into space, and fired a bullet.  Newton’s first law of motion says that bullet will travel forever in the same speed and direction, unless hindered by something like spacedust or diverted by the gravitational pull of a planet or star.  (You would also go flying backward when you fired the bullet, but that’s a subject for another time.)

Photons work the same way.  They keep going full strength until impeded.  That’s why the light from the sun isn’t attenuated by the time it hits the earth.

My parents, taken with a point-and-shoot
with pop-up flash.  Under these conditions, if the subjects are different distances away, only one will be exposed correctly.

And yet for years I’ve been teaching photography students about the Inverse Square Law, which states that the light gets weaker the further away it gets from the light source.  (And I gave several examples proving this law, like the image of my parents on the right!)  Have I been peddling a lie all of these years? 

The answer is both yes and no.  People experience the inverse square law all the time, especially back in the days when cameras had pop-up flashes and people used it as the sole source of light in a dark room.  (See example.)  Here, if there are multiple people in the shot, it’s important that all subjects are the same distance from the flash, for if the distances are different, only one of them will be illuminated “properly” – the rest will be too dark.  

Why is that?  Why don’t all of the photons travel forever unless unimpeded?  The answer isn’t because the light is getting weaker; it’s because the light is spreading out.  Have a look at the figure below.  As the light travels away from the point source, it spreads out.  The total amount of illumination is still there, it’s just spread over a larger area the further away it gets.  So if you were to take a light meter and measure a specific point at various distances away, the light intensity at that specific point will be lower.  And the further away you get, the more the light spreads out, and the lower that one specific point will register on the light meter.  But the total amount of light a given distance away remains the same.  So it’s not violating any basic laws of physics.  

THIS is what's really going on.  The light is
spreading out, so the total amount of light
gets distributed in a larger area.

But can it be said to be a law when there are so many exceptions?  There are three blanket scenarios where the light falloff doesn’t adhere to this well known ‘law’:

1) Lasers

This is the most common counter-example.  Laser light is famous for barely spreading out at all, allowing you to shine it at the moon and still retaining its intensity.  The reason for this is that laser light is “collimated”, meaning it shines in only one direction and, unlike light from a point source, has no inclination of spreading out.  

(Well, that’s a bit oversimplified…  lasers do spread out, but not as rapidly as light from an incoherent light source such as a flashlight.  A few websites point out that the Inverse Square Law equation for lasers has a constant associated with it: 1.96 x 10^7.  So for practical purposes the law doesn’t really apply.)

2) Lights with Parabolic Reflectors

Examples of this are searchlights, or softboxes with a parabolic reflector.  Instead of having the light spread out, a parabolic reflector sends all light rays in the same direction, which in theory will attenuate the light dispersion.  (“In theory” because parallel light rays don’t exist in real life.  They will always diverge or converge slightly.)  These kinds of lights don’t spread out nearly as much as a point-source of light, and therefore the inverse-square law doesn’t apply to them.  

3) Lights whose surface area is significantly larger than the distance between light and subject

A third, rarely-discussed scenario is where the size of the light source (a flat panel, for instance, or an overcast sky) is significantly larger and/or closer than the subject being photographed.  (See example from the Filmgear LED Flo-Box).  In instances like this, empirical evidence says that the light loss is 1/d instead of 1/d2.

But What About the Subject-Camera Distance?

Interestingly, all of this light falloff calculation stuff only applies to the light that goes between the light source and the subject; it does NOT apply to the light that bounces off the subject and goes back to the camera.  In that case the exposure for that bounced light remains the same even if the camera changes distance or position.  How can that be?

Let’s do a thought experiment.  Let’s say you double the distance between the camera and the subject, so you will have effectively 1/4 of the amount of light hitting the sensor (the inverse square law). BUT the area of the subject on the sensor that SAME LIGHT HITS has diminished by 1/4 as well (1/2 the height times 1/2 the length makes for 1/4 the area).  So basically even if the light gets weaker by a factor of 4 (reflected or not), the SURFACE it has to expose diminishes by the SAME FACTOR, which makes that the exposure value stays the same.

Unintuitive, huh?

In the Pipeline

Free supplements have been distributed to owners of the Sony A1 and A9 III cameras, both covering their respective new features in Firmware update v3.0.  If you didn't receive one, email me your purchase receipt and I'll send you the supplement.

The Sony A1 II ebook is still in the works.  (I'm still waiting for mine to arrive... Current rumors say no new units will ship in the U.S. until April, and Sony Pro Support hasn't had any to loan out.)  In the meantime you can Pre-order your copy now at a discount! 

Upcoming Seminars 

Surely you're familiar with the Friedman Archives High-Impact Photography Seminars by now!!  The next one is being planned for San Jose, California - April 26-27, 2025   Email me (Gary at Friedman Archives dot com) if you're interested or if you know of a camera club in the area!  

Next time in CameraCraft Magazine

I sit down for an interview with legendary photojournalist David H. Wells, whose 50-year career spanned several newspapers, LIFE magazine, National Geographic, Newsweek, The Sunday New York Times, Fortune, and Time.  Nominiated for a Pulitzer prize, he splits his time between his home in the US and in India, where he's been teaching and working on several personal projects.  I also talk to him about his pivot to short films.

Subscribe to Cameracraft magazine today!  (In either print or digital form!)

Kenya Trip Report

Back in December I gave you a small glimpse of the Photo Safari I hosted in Kenya.  Absolutely everyone loved it, so much so that they all want to do it again in November.  I thought I'd go into some more detail about the experience, since there will be a few extra slots this year.

The Accommodations

Glamping at its finest.

The best way to describe our accommodations was “glamping” – high-end tents, extraordinarily clean, fresh bedsheets and a private bathroom with western toilet.  Showers had to be scheduled ahead of time, at which time someone would come with one large bucket of hot water and one of cold, pour them both into a large canvas bag, then raise the bag up for potential energy.  The showers were actually quite pleasant!

Each day was similarly structured...  Breakfast at 7 AM, then embark on a morning safari (when it was still cool out); lunch at 1 PM, then a siesta until early afternoon.  Afternoon safari would then commence; then dinner at 7, then sometimes an evening outing after dinner.  Evening safaris are accompanied by near-IR spotlights from the jeep, so as not to disturb the animals too much but still make them photographable.

Lots of animals out our tent screen.

Sounds like a packed schedule, yet there was lots of time for socializing.  (As it turns out, my readers are very friendly people! J ) 

One thing there really wasn’t time for, ironically, was to go through our pictures and share best ones.  There were simply too many images to plow through – all I had time to do was empty my memory cards, make a backup, then go socialize (or get some sleep).  The great philosopher Kenny Rogers taught us that you don’t count your money when you’re sittin’ at the table.  They’ll be time enough for countin’ (or picture going throughin’) when the safari’s done.

Relaxing after a full day of shooting.

Delivering hot and cold water for the showers.

Monkeys were everywhere.  They broke into our tent
twice and stole our trail mix!

  The Food

On the plus side, the food was delicious and very western.  Gourmet chefs prepared 3-course meals including desserts which everyone enjoyed.  On the minus side, if we wanted to taste local cuisine, we’d have to go elsewhere.  Sometimes we'd eat at the camp; often times tables were set up in the bush and we'd feast outdoors.  And if you like alcohol, there's plenty to be had - all included!

The Staff

This, I think, was the best part – in order to work at a Gamewatchers camp you have to take a 2-year school where you learn encyclopedic-level knowledge of all the animals, their habits, movements, and after awhile, their social order.  Not just knowledgeable tour guides, they all understand the importance of good light to a photographer and go out of their way to drive the jeep close to the animals with the sun in the right direction. 

But in terms of helpfulness, absolutely everyone in the camp went above and beyond, whether it’s wiring up a tent with electricity to accommodate a CPAP machine, to sending a forgotten iPad to the airport in time for departure, absolutely everyone made sure we had a great trip.

Same Time Next Year?

Everyone had such a good time that we all vowed to do it again in November 2025!  Details are still congealing, but if you're thinking of joining us this year please send me an email at Gary at Friedman Archives dot com and I’ll put you on the notification list.

You can see my favorite pictures here.  And some of the favorite photos from the participants here.

It is a trip we will remember forever.

More in Uganda

I'm hoping to be heading back to Uganda in early March to follow up on the story I told you in January.  There is much more of the story to tell.  Stay tuned!

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Until next time,

Yours Truly, Gary Friedman