# inverse ssquare law

Discussion in 'Lighting' started by RalphLambrecht, Mar 6, 2014.

1. ### RalphLambrechtSubscriber

Messages:
8,729
Joined:
Sep 19, 2003
Location:
fl,USA
Shooter:
Multi Format
This is confusing me
according to the inverse square lawB=I/d^2,theIllumination from a light sourcequadruples every time the distance from subject to light source is cut in half.Inconsequence doesn't that mean that the light source approaches infinite intensitywhen the distance to the light source approaches '0'?Hoew can this be?is there a flaw in the inverse square lawor is it limited to certain conditions?:confused:

2. ### Dr CroubieMember

Messages:
1,994
Joined:
Mar 21, 2013
Location:
Shooter:
Multi Format
ooh, physics!
yeah, you're somewhat right, basically it's asymptotic. Half the distance and you quadruple the intensity. Keep halving and you keep quadrupling, until you're infinitely close and light is infinitely intense.
But as with most physics, there is a basic assumption, in that it's a point light source, which don't exist in reality. Get closer to the bulb and the bulb gets comparatively "larger".

Even if you consider a single excited electron emitting single photons as it changes excitation levels, as you get closer and closer to within a few nm you enter the realm of quantum physics (where my 1st-year knowledge ends) and the whole thing falls apart. I think you'll need a Sheldon for a GUT or String Theory explanation past that...

3. ### fretlessdavisMember

Messages:
314
Joined:
Dec 28, 2013
Location:
Southern AZ
Shooter:
Medium Format
I did a lot of sound wave stuff in my studies (Physics-- I didn't do as much with light or optics). Sound Pressure uses a very similar formula, and the baseline is measure at 1 meter.

It's a valid formula, that does in fact approach infinity, as it cannot be divided by 0. The formula assumes a true point source, though, so the area of illumination at such fractional distances would be nill. If you were measuring light hitting a spec of dust, you could get it much closer to the point source before it wouldn't be illuminated. It assumes a total illumination of the subject, which is constant, through the distance.

4. ### fretlessdavisMember

Messages:
314
Joined:
Dec 28, 2013
Location:
Southern AZ
Shooter:
Medium Format
You beat me to it!

But yes, the law applies with the same size subject, and assuming a point light source.

Physics is an exact science in a frictionless vacuum, once you bring it into the real world, the small inaccuracies are small enough to not really affect things at the distances we use in photography.

5. ### MattKingSubscriber

Messages:
19,426
Joined:
Apr 24, 2005
Location:
Shooter:
Multi Format
It is much more helpful if you use the inverse square law to predict how light intensity decreases as distance from the source increases.

That way you don't run into problems with the fact that the law only applies completely to impossibly small, point light sources.

6. ### snapguyMember

Messages:
1,294
Joined:
Jan 1, 2014
Location:
California d
Shooter:
35mm
loss

I am at a loss on how to determine how this relates to my 110-film Teenage Mutant Ninja Turtles flash unit.

7. ### fretlessdavisMember

Messages:
314
Joined:
Dec 28, 2013
Location:
Southern AZ
Shooter:
Medium Format
Same thing with everything I did in acoustics. SPL is standardized at being measured at 1m for speakers and such... makes up for the errors in not having sound coming from a point source...

8. ### Dr CroubieMember

Messages:
1,994
Joined:
Mar 21, 2013
Location:
Shooter:
Multi Format
hehehe, frictionless vacuum

9. ### fretlessdavisMember

Messages:
314
Joined:
Dec 28, 2013
Location:
Southern AZ
Shooter:
Medium Format
EVERYTHING works in a frictionless vacuum, except, you know, just about everything.

EDIT: I almost posted the same comic with my post. Gotta love XKCD.

10. ### ntennyMember

Messages:
2,282
Joined:
Mar 5, 2008
Location:
San Diego, C
Shooter:
Multi Format
Look at it this way---a certain amount of light is distributed over a sphere, and the intensity is the amount of light divided by the surface area of that sphere. If the distance were zero, what would that surface area be? Zero. So you really *would* have a light of infinite intensity at that point, in the "assume a spherical cow" world that the equation models.

-NT

11. ### markbarendtSubscriber

Messages:
8,652
Joined:
May 18, 2008
Location:
Beaverton, OR
Shooter:
Multi Format
The formula basically says that light spreads out as it moves away from the source. The rays move in straight lines.

The closer you get to the source, the more light rays you block. (Your shadow gets bigger)

12. ### Dave SwinnardSubscriber

Messages:
266
Joined:
Sep 8, 2002
Location:
Parksville,
Shooter:
Multi Format
Ralph, for another similar, but opposite issue, check Olbers' Paradox...

13. ### ambakerMember

Messages:
666
Joined:
May 6, 2011
Location:
Missouri, US
Shooter:
Multi Format
As mentioned above, the inverse square law is designed to explain how the level drops as you move away from the source. However, another factor not often mentioned is that a point source is not considered a point source until you are 1/2 the length of the source, distant from the source.

So, if you have a flash tube 2 inches long, it does not become a point source until you are 1 inch away. Closer than 1 inch it becomes a line source. With its own set of rules.

Gotta love electromagnetic radiation. It paid my bills for a lot of years.

Sent from my iPad using Tapatalk HD

15. ### NedLSubscriber

Messages:
2,097
Joined:
Aug 23, 2012
Location:
Sonoma County, California
Shooter:
Multi Format
I think Zeno said it was pretty bright when he got there.

16. ### KawaiithulhuSubscriber

Messages:
359
Joined:
Sep 20, 2013
Location:
Southern Cal
Shooter:
Multi Format
Look at it the other way around, not at how much more bright the light is the closer you get but how much darker the light gets the further away you go.

So standing at 0 from a point light source you are losing 1/0 (aka not even a number) and that means that the light is as bright as the energy it outputs. Move back and stand 2 away and now you are losing 1/2^2 (aka one-quarter) of the original brightness. Stand 4 away and your light is now 1/4^4 (aka one-sixteenth) lost. Etc.

17. ### lxdudeMember

Messages:
6,906
Joined:
Apr 8, 2009
Location:
Redlands, So
Shooter:
Multi Format
The law of inverse squares states that at least once, any nerd in high school will be put upside down in a trash can by a football player.

18. ### jccMember

Messages:
494
Joined:
Jul 18, 2012
Location:
Norman, Okla
Shooter:
Multi Format
Pretty sure the question was already answered, so I'll just my two cents... Physics loves math, but math could care less about physics.

19. ### StoneNYCSubscriber

Messages:
8,239
Joined:
Aug 5, 2012
Location:
Connecticut,
Shooter:
8x10 Format
You have to think of it this way Ralph, forget the point light source, forget the distances, no matter how many times you "get closer" you can never actually be at 0 because two things cannot occupy the same space at the same time, and also you will always be 1/4th (or whatever the opposite of quadruple) away from the light source ALWAYS, you will never hit 0 and will never reach the light... It's impossible.

20. ### MattKingSubscriber

Messages:
19,426
Joined:
Apr 24, 2005
Location:
Shooter:
Multi Format
Stone:

Take some university physics courses and you will find that what you say here isn't actually true.

Or for that matter, watch a few Star Trek episodes .

21. ### StoneNYCSubscriber

Messages:
8,239
Joined:
Aug 5, 2012
Location:
Connecticut,
Shooter:
8x10 Format
My dad is a real honest to god physicist... I'll ask him tomorrow...

22. ### Tom1956Inactive

Messages:
2,024
Joined:
May 6, 2013
Location:
US
Shooter:
Large Format
Stone, you're wrong on 2 counts: firstly politicians do it every day when they make a speech. Secondly, when you walk up to the Sun and put your light meter on the surface and take a reading. THAT is point zero. You're not interested in digging through 433 thousand miles of plasma with a shovel to get the "true" reading.

23. ### Steve SmithMember

Messages:
9,128
Joined:
May 3, 2006
Location:
Ryde, Isle o
Shooter:
Medium Format
SPL can be measured at any distance. It's usually one metre and one watt to work out speaker efficiency.

Steve.

24. ### StoneNYCSubscriber

Messages:
8,239
Joined:
Aug 5, 2012
Location:
Connecticut,
Shooter:
8x10 Format
That meter (if it does t melt) can hover just above the surface but will never be INSIDE the light point, it's impossible, can't occupy the same space, just making quarters and quarters closer for infinity...

25. ### CurtMember

Messages:
4,560
Joined:
Sep 22, 2005
Location:
Pacific Nort
Shooter:
Multi Format



Approaching
Sometimes you can't work something out directly ... but you can see what it should be as you get closer and closer!
Let's use this function as an example:

(x2-1)/(x-1)

And let's work it out for x=1:

(12-1)/(1-1) = (1-1)/(1-1) = 0/0

Now 0/0 is a difficulty! We don't really know the value of 0/0, so we need another way of answering this.

So instead of trying to work it out for x=1 let's try approaching it closer and closer:

x (x2-1)/(x-1)
0.5 1.50000
0.9 1.90000
0.99 1.99000
0.999 1.99900
0.9999 1.99990
0.99999 1.99999
... ...
Now we can see that as x gets close to 1, then (x2-1)/(x-1) gets close to 2

We are now faced with an interesting situation:

When x=1 we don't know the answer (it is indeterminate)
But we can see that it is going to be 2
We want to give the answer "2" but can't, so instead mathematicians say exactly what is going on by using the special word "limit"

The limit of (x2-1)/(x-1) as x approaches 1 is 2

So it is a special way of saying, "ignoring what happens when you get there, but as you get closer and closer the answer gets closer and closer to 2"

26. ### lxdudeMember

Messages:
6,906
Joined:
Apr 8, 2009
Location:
Redlands, So
Shooter:
Multi Format
Actually, the answer to everything is 42.