This post is taken from an email I received from the cinematographer mailing list. It is a humourous and well written explanation of the inverse square rule of light.

The Inverse Square Law... yes... it's about calculating how bright a light will be. That's the real world application. By the way it's also know as the Law of Squares.

Let's say you want to put a light on a rooftop across the street from where you are shooting to simulate moonlight.... moonlight comes from above, right?... so you want the light high up. You can't afford a lift that can raise the light high in the air, so you tell your lowly electricians (that's me) to haul the big light up the interior stairs of the building and "just bloody well get it up there". The electricians might all quit because of your nasty way of saying it but they are all poor schmucks who are afraid of big Directors of Photography like you... so... they just do as they are told.

Now, you are not sure what F-stop to shoot at... should you use really fast fast film (which has lots of "bad" film graininess) or the slower stuff that looks better? Hmmm.... well, it would help to know how much light will be falling on your subject... that way you can figure out what f-stop you would be shooting. If you figure out that you are shooting a F 0.7... well, that limits your choices for lenses big time (very few are made to work at F 0.7). So then you would think to yourself... that light I thought would work over on that roof... she is going to have to be bigger! Much bigger!

But back to the inverse square law... if you know (from reading the manufacturer's specs) that a 10,000Watt light will give you X foot candles at a certain distance (foot candles are a measurement of light whichsays that a "standard candle" will put 1 footcandle of light on an object 1 foot away) you can then figure out how many foot candles will be at twice that distance. How? Using the inverse square law of course! The law says that as the distance of the light FROM THE SUBJECT increases... the amount of light reaching the same subject will decrease in proportion to the square of the distance from the subject. That's an annoying way of saying that if you know a 20,000 watt light will give you 200 foot candles at 75 feet (you know this from the manufacturer's specifications which you looked up online) then at 150 feet (which is the distance from the subject to the light across the street on top of the roof) the light will be twice as far and...

150 feet is twice 75 feet... so that's 2x as far... the amount of light will be the square of 2... which is 4...

the number of foot candles reaching our subject will only be 1/4 of 200....

or... the amount of light reaching our subject will be 1/4 of 200 foot candles which is 50 foot candles.

Now to figure out how much that all is in F-stops... F-stops after all are the units of measurement that are written on the lenses and are generally used in those fancy light meters all the Directors of Photography have these days. (If you don't know what an F-stop is... well, I'm not going to get into that here... this would take all week!) We know from... well, who knows how we know it... but somebody knows that if you have 100 foot candles of light hitting a subject and you are using 100ASA film... your light meter will tell you that you will need to shoot at an F 2.8 to expose your subject properly. So if, in our real life shooting situation, we only have 50 foot candles coming from our big 20,000 watt light across the street... then the light meter will tell us we have to shoot at a F 2.0.

Tada! We now know we will be okay to shoot with 100 ASA film... F 2.0 is plenty of light and we are good to go.... lots of lenses are made to shoot at a F 2.0, after all.

PS - I have completely made up the number for how much light a 20,000 watt light will deliver 150 feet away... you will not be able to use 100 ASA film at night with only a 20,000 watt light on the rooftop across the street, let me assure you of that. Okay..... maybe you could, but you'd be crazy! But that was not the point... the point was that to learn about the inverse square law. I hope this helped.

Piotr Jagninski
Gaffer - New York City

There you have it.

Laters

P.S. To Piotr Jagninski I apologise if you see this post and I have not asked your permission, I only do this for the sake of education of my self and fellow filmmakers who may see this blog. If you see it and wish it removed please contact me or leave a comment.