inverse ssquare law

RalphLambrecht · Mar 6, 2014

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:

Dr Croubie · Mar 6, 2014

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...

fretlessdavis · Mar 6, 2014

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.

fretlessdavis · Mar 6, 2014

Dr Croubie said:
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...

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.

MattKing · Mar 6, 2014

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.

snapguy · Mar 6, 2014

loss

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

fretlessdavis · Mar 6, 2014

MattKing said:
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.

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...

Dr Croubie · Mar 6, 2014

fretlessdavis said:
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.

hehehe, frictionless vacuum

fretlessdavis · Mar 6, 2014

Dr Croubie said:
hehehe, frictionless vacuum

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.

ntenny · Mar 6, 2014

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

markbarendt · Mar 6, 2014

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)

Dave Swinnard · Mar 6, 2014

Ralph, for another similar, but opposite issue, check Olbers' Paradox...

ambaker · Mar 6, 2014

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

NedL · Mar 6, 2014

I think Zeno said it was pretty bright when he got there.

Kawaiithulhu · Mar 7, 2014

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.

lxdude · Mar 7, 2014

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.

jcc · Mar 7, 2014

Pretty sure the question was already answered, so I'll just my two cents... Physics loves math, but math could care less about physics.

StoneNYC · Mar 7, 2014

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.

MattKing · Mar 7, 2014

StoneNYC said:
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.

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 .

StoneNYC · Mar 7, 2014

MattKing said:
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 .

My dad is a real honest to god physicist... I'll ask him tomorrow...

Tom1956 · Mar 7, 2014

StoneNYC said:
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.

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.

Steve Smith · Mar 7, 2014

fretlessdavis said:
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...

SPL can be measured at any distance. It's usually one metre and one watt to work out speaker efficiency.

Steve.

StoneNYC · Mar 7, 2014

Tom1956 said:
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.

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...

Curt · Mar 7, 2014

StoneNYC said:
My dad is a real honest to god physicist... I'll ask him tomorrow...

Stone, ask your dad how the concept of "limits" fits into the ISL.

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"

lxdude · Mar 7, 2014

Curt said:
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"

Actually, the answer to everything is 42.

inverse ssquare law

RalphLambrecht

Dr Croubie

fretlessdavis

fretlessdavis

MattKing

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snapguy

fretlessdavis

Dr Croubie

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ntenny

markbarendt

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ambaker

NedL

Kawaiithulhu

lxdude

jcc

StoneNYC

MattKing

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StoneNYC

Tom1956

Steve Smith

StoneNYC

Curt

lxdude

inverse ssquare law

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