Is there a difference between a large, far light source, and a small, close one?

As I was doing my reverse engineering of the lighting for this question, I wondered whether there's any discernable difference between a large light modifier far away versus a small light modifier close up. (This is outside the obvious things like required flash power.)

Previously, my understanding was that, all other things being equal, the factors that produce the same apparent size & light intensity were completely interchangeable. I'm wondering now if that's actually the case.

I'm thinking specifically about light falloff, due to the inverse square law. I wondered if the light from a close source might fall off faster (ie: go from bright to dark in a shorter distance) because the distance to the source itself is closer. Given a certain distance lit (such as the model's face), the ratio between it and the distance to the light source is going to be much higher for a close source than a far one... so it might make the falloff more pronounced. But I'm not sure of this by any means.

Is this correct? Are there other factors to that change based on apparent size?

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Just to clarify, are you asking about two light sources that have the same apparent size to the subject and same intensity at the subject? – rfusca Aug 8 '11 at 23:26
@rfusca: yup, "apparent" is the word I want. Editing now. – Craig Walker Aug 8 '11 at 23:27

Yes, a closer light will fall off faster due to the inverse square law. For a very close light, one cheek of your subject will be relatively much closer than the other. With a larger light further away, the distances will be much more similar, so less fall off. This will make a difference to the apparent softness of the light.

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I am not sure... the assumption is that the closer light is weaker, so in total the fall off is the same (as rfusca mentions). However, I am not convinced myself yet :-) – ysap Aug 9 '11 at 2:16
No, the light falloff is not the same. The closer light source will have more falloff. Let's say you set up two lights, one close and one far, so that the amount of light hitting the near cheek of your subject's face is the same. With the far off light, the brightness of the light hitting the far cheeck will be almost the same, but with the closer light, there will be more falloff. This is why if you want a dark background, you move the light close to the subject (more falloff) and try to move the subject away from the background. – MikeW Aug 9 '11 at 3:22
OK, you convinced me. – ysap Aug 9 '11 at 5:54
+1 for a simple explanation without formulas! It's well known that a distant lightsource will give a more even light than a close one, even if the apparent sizes are the same – Matt Grum Aug 9 '11 at 9:56

They say a picture paints a thousand words, so I'll augment the existing answers with a basic MS Paint representation.

The falloff is depicted by the yellow curves below the light paths. It's very rough, but given an 1/r² falloff, you can see how the falloff is much more gradual from the light source furthest from the subject.

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To be very precise, I think that if two sources have the same apparent size, then the farthest source will cast softer light. The apparent size is determined by the angle of view of the object (the source).

Imagine two light sources, at distance D and size H and at distance 2xD and size 2xH. Also, imagine the subject's head is of size 1.5xH. It is easy to see that although to the subject's eye the two sources appear the same size, the light falling from the far source "wraps" around the subject's head, while the light from the near source does not.

UPDATE: here's a sketch to show what mean by "wrapping". The bigger light source illuminates the subject beyond its equator, while the smaller does not:

UPDATE 2: updated the diagram to make it more geometrically precise.

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I'm not sure I really buy this. By this definition, the sun should sufficiently wrap around everything - being a very, very far point light source. – rfusca Aug 9 '11 at 2:29
@rfusca - The sun indeed wraps around all spherical objects which are smaller than itself. However, the further away the object, the less this wrapping will be beyond the day-night "equator". Also note that due to the atmosphere, this effect is somewhat eliminated by the scattering of light by in the atmosphere (which is why we have light before sunrise and after sunset). – ysap Aug 9 '11 at 2:43
I'm confused about your argument then, you seem to be saying that distance plays increases 'wrap around'. – rfusca Aug 9 '11 at 2:56
@ysap they wouldn't look the same size. The lines going from the sources to the subject are different angular sizes. I'm not arguing that the diagram is incorrect. It isn't. But the question isn't the same as what that diagram is depicting. – Nick Bedford Nov 3 '11 at 5:41
@NickBedford - You actually made me go and update the diagram. Hopefully it is clear now that the apparent size of the two sources is the same (from a cyclop's point of view...), while the lighting effect is different. – ysap Nov 3 '11 at 6:14

If the apparent size of the light is the same, then the light will appear the same, with a few exceptions.

1. The close light source might be close enough where the angles are different to different areas.
2. The closer light source might allow for some reflection off of other surfaces, which would have different effects.
3. The angle at which the light spreads might cause some different shadows to appear. Think a small light right on a person's nose, vs a huge light far away. The far away light will have parallel rays, the close light will give different shadows.
4. If the subject is large, say, a room or landscape, then the further away light source will more evenly light the subject than a close light source.

But in general, it shouldn't make much of a difference.

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