## Monday, November 19, 2012

### The Inverse Square Law (part 1) - in plain English

When it comes to flash photography, or studio lighting, you won't get very far before someone mentions the dreaded 'Inverse Square Law', and then starts quoting lighting ratios and f-stops of dropoff, and all sorts of frightening sounding stuff.  I must admit, I was full of trepidation when I first tried to understand it, and I was left with only a feeling of vague understanding, and lacking that 'eureka' feeling that I had completely grasped the concept.

It is a hard subject to describe without getting bogged down with all the technical details, but the concept itself is actually very easy to understand.  Once you get the concept clear in your mind, then attacking the technical side becomes a whole lot less scary.  So - that's what this post sets out to do - explain what it means in a practical sense, explain the concept, and finally explain (in simple terms) the technical bit with real examples.  I'll split it into two parts, so as not to fry your brain...

I'll start by stating the basic rules of application, and then explain why these work the way they do.

• If you want your subject against a really dark background, have the light source close to the subject, and the subject far from the background.
• Alternatively, if you want the subject and background with similar exposure, then have them relatively close together, and the light source some distance away (maybe 5 to 10 times the distance between the subject and background).
• Finally, if you want the background just a little darker than the subject, then have the background a similar distance behind the subject as the light source is in front.

The rules above won't mean much to you until you either try them out and see them working, or read on to get an appreciation of how these results come about.

In order to help visualise this, try an experiment.  Get a light source of some kind - anything will do, a desk lamp, a torch, anything.  Now, in a darkened room, set your light source up next to a light coloured wall, pointing along the wall.  Step back and observe the brightness of the light falling on the wall at various distances from the light itself.  Close to the light, it will be very bright, but it will quite rapidly get less bright, and then less bright again, and again... Obviously, in real life, this is a gradient rather than 'steps', but to help understand the concept, let's break up this gradient up into four imaginary brightness areas - "really bright", "quite bright still", "getting darker", and "pretty dim".

OK - here is the important bit.  Let's measure the distance from the light that falls into the category of "really bright", and for argument's sake, say it is 30cm.  Now measure the distance from there to the end of the "quite bright still" area, and this might be 1 metre.  The length of the "getting darker" area might be 3.5 metres, and the "pretty dim" area might extend for another 8 metres.

Now - I just made these numbers up to illustrate a point - and that is that the rate at which the light fades is not constant.  It drops off very quickly at the start, and then less and less quickly.  The key thing to understand here is that if your subject is quite close to the source of light, somewhere in the "really bright" area, and you move it away from the light by 30cm, it will have a radical affect on the exposure, as the level of light is changing very quickly at this distance, and the subject will now only be in the "quite bright" area.  However, if your subject is 5 metres from the light, and you move it back by 30cm, it will have much less impact on the exposure, because the light level is changing much slower at this distance, and the subject will have been in the "pretty dim" area the whole time.

Let me just state that again - in fewer words this time, without the explanation.  A small change in the light to subject distance when close to the light source, will require a big difference in exposure.  The same change in distance when further away from the light source, will require only a small difference in exposure (if at all!)  Savvy?

Now that (I hope) you have begun to grasp the concept, let's give you some real figures so you can appreciate what it means to your camera settings, and start to understand the real life scenario.  But first of all, close your eyes, and drift into dream mode, and come on over to my studio, where I have a nice strobe in a big soft box set up for you, with Cactus V5 radio triggers, and you'll have a great camera in your hands (of course, that would be a Nikon D3000, wouldn't it?) Pssst - now, open your eyes again so you can carry on reading!!

So here in my studio, sitting 1 metre in front of the softbox, is your subject.  It could be a beautiful girl, a handsome guy, or a bottle of beer someone brought to Australia for you from England (hic!) - yes, let's go with that one.  You set up your camera to expose the bottle perfectly, and take the shot.

NB - From now on, all the distances we talk about will be in multiples of the distance from light to subject (which in this case, is nice and conveniently 1 metre).  I'll call these 'distance units', but remember, it is just the distance from the light source to the subject.

Now place another bottle of beer 1 distance unit (e.g. 1 metre) behind the first, and take another shot without changing any settings, and... whoa - where's my second beer gone!?  Being 1 distance unit further away, there is only 1/4 of the light reaching the second bottle - that is 2 stops of light lost over the first unit of distance.

Now let's move the second bottle back another distance unit, so it is now 3 distance units (3 metres) from the light.  At this distance, only 1/9th of the light is reaching the it.  Now the interesting thing is that although you doubled the distance, you have only lost a little over 1 stop of light this time.

Another metre (or distance unit) back, and now just 1/16th of the light is reaching the second bottle, but this unit cost you even less than one stop of light.

From here on, the loss of light is becoming more and more negligible.  You can now go another FOUR distance units, and only lose 2 stops of light.  Remember - you previously lost 2 stops of light just in that first unit!

Hopefully, you are getting the idea...?  Good.  Now, take a break, and come back in a few days for part two (when I've had a chance to create a few more graphics).

TTFN
Grum