The Inverse Square Law

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The Inverse Square Law

Postby scottwramsay » Mon Sep 07, 2009 2:10 pm

Briefly - since my battery is dying - I was on the Basic Studio Photography course at the Met. The instructor was discussing which lens to use for portraiture and recommended about 70mm because shorter would give you distortion and longer would require you to be standing on the other side of the room, killing any creative atmosphere.

This got me thinking - wouldn't you need to change your exposure settings or increase your flash power to compensate if you moved away from the light source? I tried voicing my concerns but no-one in the class seemed to have been taught to think of light as discrete and quantifiable rather than "it's just there and you turn up the bulb to make it brighter". They all looked at me like I was crazy and the instructor said "trust me, you'll go away and think about it and one day you'll think 'ah, yeah, he was totally right'. Since we'd been shown that the studio lights had power dials marked in stops and begun to think about how if you turn up the light you'll have to close down your aperture to maintain an exposure, I thought why doesn't this apply to distance from the subject?

So here's my problem - if I move twice the distance away, the inverse square law says that I'm going to have a quarter the number of photons passing the end of my lens. Yet the before and after photo look the same. I've got a feeling that it's either something to do with the fact that as I move away I'm also zooming back in to keep the framing the same, or (suggested by a physics graduate, though admittedly he works on astronomy and gravitational waves) I'm so close relative to the light levels that the distances between my start and end positions are negligible.

Help?
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Re: The Inverse Square Law

Postby scottwramsay » Mon Sep 07, 2009 2:11 pm

That wasn't so brief after all.
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Re: The Inverse Square Law

Postby bobrobert » Wed Sep 09, 2009 9:11 am

You seem to be making a mountain out of a molehill. You set the aperture for depth of field. Large for shallow depth, if that is what you want and the camera will select the shutter speed. As long as it isn't too slow to hand hold without blurring. Every thing else will be taken care of. Moving in or out will only affect the depth of field and the amount of blurring in the background. :)
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Re: The Inverse Square Law

Postby BrigitDoon » Wed Sep 09, 2009 11:13 am

Zoom in and watch what happens to the shutter speed. It will compensate. The inverse square law does apply. Twice the distance away means a quarter of the light is reaching your lens.
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Re: The Inverse Square Law

Postby scottwramsay » Wed Sep 09, 2009 11:32 am

bobrobert wrote:You seem to be making a mountain out of a molehill...if that is what you want and the camera will select the shutter speed


I'm talking about using the camera on full automatic in a studio. Maybe I should have made it clear that in the studio shutter speed don't make much difference, since the flash only persists for an instant.

BrigitDoon wrote:Zoom in and watch what happens to the shutter speed. It will compensate. The inverse square law does apply. Twice the distance away means a quarter of the light is reaching your lens.


Right well that leaves me in a bit of a funny place then - I was right and the instructor was wrong, but the photos were still OK... I wish I could get back in and have a play around again.

Harumph.
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Re: The Inverse Square Law

Postby potatojunkie » Wed Sep 09, 2009 3:11 pm

The inverse square law applies only to point sources. What was the lighting setup? Were any diffusing materials involved?
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Re: The Inverse Square Law

Postby scottwramsay » Wed Sep 09, 2009 8:13 pm

Ah-hah, that might be the penny on the floor.

It was something like this:
Code: Select all
//////////////////////////////////////////////////
------------------White backdrop------------------

    \      /                         \      /
     \    /                           \    /
        x                                x
---White board---               ----White board---

                         O
                        \|/
                         |
                        / \             
                                       \
                                        \
                                    _____x (probably with a softbox)





                        O
                     __ ||__
                    |_______|
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Re: The Inverse Square Law

Postby scottwramsay » Wed Sep 09, 2009 8:21 pm

That'll be it I reckon, definitely. Looks like the physicist was right about being too close for it to matter, except he wasn't really sure that he was right...

If anyone else is curious, I followed up PJ's post with a trip down Wikipedia lane. Here's an extract from the Inverse Square Law page as applied to photography:

a "point source" (subject to 1% error) is obtained from a "psuedo[sic]-point-source"...at a distance 10 times the source radius (5 times the diameter). A four-foot fluorescent lamp is (almost) a point source (subject to 1% error) at a distance of 20 feet. Similarly, as one gets closer to a fluorescent lamp the apparent brightness will increase up to a certain distance (because the viewing angle (sampled area) remains constant and closeup (1 foot away) the entire fluorescent tube can not be viewed), after which the intensity will not continue to increase (as it would with a (pseudo) point source).


I guess since the backdrop was much larger than a 4-foot fluorescent lamp, I'd have to have been a helluva lot further than 20 feet away for it to start having an effect. About 50 feet, by my estimation (subject to 1% error, of course).


(P.S. How come we can't do strikethrough text? Or can we?)
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Re: The Inverse Square Law

Postby hungryjoe » Mon Sep 14, 2009 2:14 pm

What a mountain out of a molehill.

As someone has correctly pointed out, the Law Of Inverse Square applies where a point source of energy is used, in this case, light.

That law will only be invoked if the source of illumination is moved closer too, or further from, the subject. The distance between the camera and the subject doesn't matter. If the illumination is moved, there are simpler ways to calculate exposure, either with a meter (flash meter for flash), using guide numbers (a separate problem) or using (usually) on camera flash which automatically calculates how much light should be generated.


A wee edit. I was always taught, that when using a 35mm camera, the best focal length lens for portraiture is 90mm.
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Re: The Inverse Square Law

Postby scottwramsay » Mon Sep 14, 2009 2:55 pm

Joe, you're re-phrasing with what I just posted.

hungryjoe wrote:...there are simpler ways to calculate exposure, either with a meter (flash meter for flash), using guide numbers (a separate problem) or using (usually) on camera flash which automatically calculates how much light should be generated.


I agree with you there too - my point wasn't that I want to be able to calculate exposure with the inverse square law, just that no-one else seemed to understand that moving away should reduce the light reaching you.
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Re: The Inverse Square Law

Postby hungryjoe » Mon Sep 14, 2009 4:50 pm

scottwramsay wrote:Joe, you're re-phrasing with what I just posted.

hungryjoe wrote:...there are simpler ways to calculate exposure, either with a meter (flash meter for flash), using guide numbers (a separate problem) or using (usually) on camera flash which automatically calculates how much light should be generated.


I agree with you there too - my point wasn't that I want to be able to calculate exposure with the inverse square law, just that no-one else seemed to understand that moving away should reduce the light reaching you.


You are not measuring the light reaching you.

Moving away from your subject doesn't alter the amount of light falling on your subject. The only two ways I know (apart from the guide No. scenario) of determining the correct exposure are (a) measuring the amount of light falling on your subject, or (b) measuring the amount of light being reflected from your subject. It doesn't matter how far you move from your subject (assuming you can zoom in and fill the frame in the same way), if you don't move the source of illumination, the correct exposure will remain constant because the Law Of Inverse Square has not been invoked.
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Re: The Inverse Square Law

Postby scottwramsay » Tue Sep 15, 2009 5:33 pm

Hi again Joe,

hungryjoe wrote:You are not measuring the light reaching you...The only two ways I know (apart from the guide No. scenario) of determining the correct exposure are ... or (b) measuring the amount of light being reflected from your subject.


That's a wee contradition there - the light reflected from your subject is the light reaching you. Your camera circuitry absolutely measures the light coming your way, not the light hitting your subject, and if you use your handheld meter to measure reflected light you'll certainly see it drop off as you step back from the model towards your camera.

Similarly to how the moon is a source of light on a dark night, the model is the light source as far as your camera is concerned, not the studio lights. Same goes for any subject you photograph, it just gets confusing in a studio because suddenly we have a controllable sun so we run around taking measurements from it so we can adjust it.

All that aside, by jove, I think I've got it.

Had a chat with another physics PhD student who misunderstood how apertures work, but his wording reminded me that aperture size is expressed as a ratio of the hole-size to lens-length, not an absolute size. This means it's changes as you zoom. There IS less light hitting the front of the lens as you move back from your subject, but if you leave your aperture setting well alone (and your shutter speed too) and zoom back in then you actually widen the aperture compared to what you originally used.

Close up: 18mm at f/2 has a physical hole-size of 18mm/2 = 9mm.

Zoom shot: 200mm at f/2 has a hole-size of 200mm/2 = 100mm.

So you do open up your aperture to compensate for the inverse square law, but the aperture nomenclature hides it from common sense-view.

*phew* don't know who's more glad, but I'm finally satisfied :roll: .
Last edited by scottwramsay on Tue Sep 15, 2009 5:39 pm, edited 1 time in total.
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Re: The Inverse Square Law

Postby Lucky Poet » Tue Sep 15, 2009 5:36 pm

I'm trying desperately to get the idea of the light source and subject being separate things. Not that I'm doubting it, mind. Um... (Then again, I don't shoot in studios :) )
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Re: The Inverse Square Law

Postby scottwramsay » Tue Sep 15, 2009 5:40 pm

LP - I just edited my post there because I realised I missed out a bit on that!
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Re: The Inverse Square Law

Postby Lucky Poet » Tue Sep 15, 2009 5:46 pm

I didn't notice you'd posted to be honest - 'twas mainly a reply to hungryjoe :oops:

*Edit after reading the whole thread again* I'm definitely confused now and give up for the evening. Where's Ansel Adams when we need him?
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