How does the inverse square law relate to the softness of light for portraits?

I am a bit confused. I understand that if you want soft lighting for portraits, you need to use a large light source compared to the size of your subject. So, I thought by bringing the light source in close to the subject to make it larger would make it a softer light vs having the light source far away. I watched a wonderful youtube tutorial from Mark Wallace about the inverse square law. This is where the confusion comes in.

It seems to me that in his video he shows how a light that is placed close, say a couple of feet, to the subject will have far greater light fall off than one where the light is farther away. Hence having the light in close to the subject seemed to make it more contrasty. As I see it less soft.

There are two questions I hope someone can help me with:

1. Most tutorials show that when you are shooting a portrait, where the look is to have soft light, they set the lights at around 6 to 10 feet from the subject, Is this due to the inverse square law?

2. What am I missing here?

• I will try to make some diagrams for my answer, but if the video is the one inkista posted it has a metodological error: the walls of the studio are white, so the ambient bounced light from the same softbox is iluminating the face. – Rafael May 11 '16 at 15:05

Without getting into the mathematics of the situation which is covered by others with graphs and equations, let me try to clarify the difference between these two different aspects of the lighting.

Quantity and quality.

The quantity or the amount of light is determined by how far the light travels. All other things being equal, the shorter the distance the greater the amount of light falls onto the subject. The inverse-square law refers to this aspect. The formulas and graphs are an attempt to quantify the change of intensity with the distance.

The quality of the light is determined by the relative size of the source. Generally, the bigger, the softer. Some refer to soft light as "wrapping around" the subject. The transition from highlight to shadow of a soft source is gradual and smooth. As the source diameter diminishes to a spot the shadows "harden" and cast sharp, abrupt shadows. As a source gets further from the subject, its diameter relative to the subject diminishes too.

TIP:
The f/ #s on the barrel of a lens can be used to judge the depth of light fall-off - without a calculator - due to the application of the inverse-square law.
From 2.8 to 4 feet, the light will fall off 1 stop.
From 4 to 5.6 feet, the light will fall off another stop
From 5.6 to 8 feet, the light will fall off another stop
From 8 feet to 11 feet, another stop, and so on.

Using this TIP, you can see that putting a model about 6 feet from the source, gives the photographer a full 2-1/2 foot-deep zone of light that has less than a stop fall off. This is well within the lighting ratio for, and range of, flattering portrait light. (This is an application of the Inverse-Square Law)

Suppose the subject was a piece of equipment that was 3 feet wide. Placing the subject 8 feet from the source ensures that from the closest point to the furthest point of the equipment is within one stopâ€”well within the acceptable lighting ratios for product photography printed brochures. (This is another example of the Inverse-Square Law)

"Soft light" is a term used to refer to light that produces diffuse shadows rather than distinct shadows. But that doesn't mean you can't have some areas that are very dark and other areas that are very bright when using soft light. It just means the transitions from the bright areas to the dark areas are more gradual and less distinct.

The reason you want to get the light as close to the subject as possible when soft light is desired has nothing to do with the inverse square rule. Instead, it is because the closer the light source is to the subject, the larger it becomes in terms of the angular size of the light as measured from the surface of the subject. If you have a soft box at four feet from the subject it fills twice the angular distance as the same soft box would when placed at eight feet from the subject. To get the same brightness you would need to reduce the power of the light by one stop to compensate for the closer distance.

The reason a light placed closer to a subject will have greater fall off is because the ratio of the distance from the light source to the nearest part of the subject and the furthest part of the subject is greater than when the light source is more distant from the subject. Think of it in the same way as you understand compression based on shooting distance: When you are very close to a human subject the nose can be half as far from the camera as the ears. This tends to stretch the face out. When you are 20 feet from the subject the nose only about 2% closer to the camera than the ears are. This tends to flatten the face.

Placing the lights 6 to 10 feet from the subject is often desired because it allows for clear lines of sight to the subject without having to move the lights every time the photographer wishes to change the camera position. They key word here is lights, rather than light. When you are using multiple lights from both sides of the subject you are creating softer light by placing more than one light at angles far enough apart from each other to fill the shadows cast by the other light. You're essentially creating a light as wide as the distance between the far edges of each of the multiple lights. To get the same soft light effect from a single light you would need that single light source to be close enough to the subject, or large enough, to occupy just as wide of an angle as what the multiple lights combined occupy.

• I do not like much the nothing word "has nothing to do with the inverse square rule", because it has something to do. Not as the primary reason but still applies. – Rafael May 11 '16 at 14:45
• ...when soft light is required... Any change in subject brightness due to the inverse square rule can be compensated for by reducing the power level when moving closer. The reason one moves a light closer to soften the light has nothing to do with the inverse square rule, it has to do with the angle of coverage. If one is moving the light closer to increase the brightness of a light already at maximum power, then it does have something to do with the inverse square rule, but that is not the case here. We are discussing softening the light, not increasing its brightness. – Michael C May 11 '16 at 19:20
• Obviously you must apply the inverse square rule to adjust the power level, but it is not the reason moving the light closer yields softer light. Not at all! – Michael C May 11 '16 at 19:25

Assuming that the video you saw is this one, rewatch the near/far usage of the light, but pay attention to the line of the shadow on the model's face.

Note that when the model is near the softbox, that the line is wider and blurrier, i.e., softer light. But when the model is farther away from the softbox, that line becomes smaller and more defined, i.e., harder light. Sunlight is probably one of the hardest lights of all, and gives a very sharp defined line between shadow and light.

So your understanding is actually correct—the nearer to the light source, the larger the light source becomes, and the softer the light.

Falloff is something else. Falloff is transitioning from light to dark and is about light levels (not quality).

What the inverse square function is telling us is that the amount of light falloff is inversely proportional to the square of the distance. A simple Cartesian graph of the y = 1/x2 function looks like this:

So, think of how high the red line is as being how bright the light is, and how far to the right on the graph, as how far away you are from the light source. (This is why the words "inverse square" are still used, despite the mathiness—to precisely describe how much falloff you have vs. the distance from the light.)

Note that near 0 (i.e., when you're really close), the inverse square falloff is really fast and steep. So, yes, you can get a large transition in light levels at relatively small distances. When you get farther out, the curve flattens, so your falloff isn't as large—but the overall level of light is much lower—something you aren't seeing in the video, because the photographer is compensating for that with exposure settings.

The law of the invers square is only truly valid for point light sources. For photo purposes we are taking about a bare light bulb following the law almost exactly. As soon as you place this lamp in a reflector or cover it with a diffuser, the resulting light fall-off does will not strictly follow this rule. The extreme would be search light that outputs parallel light rays, the spotlight now cast a bright circle of light that remains unchanged in brilliance over extreme distances.

Now a broad light source, if it is big enough, will cast light that remains constant in intensity for a considerable distance (it does not obey at all, the law of the inverse square). Thus broads are favored to output soft light. By soft, we mean the shadows cast by the light are about the same intensity as their surrounds.

1. Via the law of the inverse square: A lamp placed 6 feet from the subject cast light that measures 100 units (watts or lamberts) reflected from the subject. If the distance, lamp to subject is increased to 6 x 1.4 to 8.4 feet, the light at the subject drops to 50 units. If the lamp is place at a distance of 10 feet, and 100 units of light is measured at the subject plane, moving the light to 10 x 1.4 = 14 feet, reduces the light to 50 units. The value 1.4 is the key. The further away the lamp the longer the span that yields a 50% reduction. Since the valleys and projections of the face are only an inch or less, the differences in light energy between the two extremes is minimal. Thus a distant lamp is less harsh.
2. You are missing that the further the lamp distance the longer the span of distance to make a 1 f/stop difference which is a 50% falloff in light level.
Factorial: A lamp obeys the law of the inverse square. Multiply lamp to subject distance by 1.4 computes the lamp to subject distance that results in a 50% decrease (1 f/stop). Divide the subject to lamp distance by 1.4 computes a revised lamp to subject distance that results in a 100% increase in light (1 f/stop) at the subject plane.

Inverse square law is only about the intensity of the light. 2x more distant is 1/4 as bright. It is NOT AT ALL just about point sources, its about softboxes and umbrellas too, IF you ignore the fabric and measure the distance to the actual flash tube. There will of course be dumb arguments, but inverse square law is NOT measured from the fabric surface, the fabric is not the light source. Only math students studying calculus like to consider the flat panel. :) Photographers have different concerns. And we generally more conveniently use light meters instead of a measuring tape.

Soft light is about the largeness of the light diameter. That is much more than just diffusion. We can use a large light, or placing it close makes it appear larger, as seen by the subject, so soft is about both close and large. It is pretty hard to get too much of either large or close.

``````A light at a distance equal to half of its size: seen as 90 degrees width
A light at same distance as its size: 53 degrees width (this will be quite soft light)
A light at 2x the distance as its size: 28 degrees width
A light at 5x the distance as its size: 11 degrees width
An 8 inch softbox at 6 feet (9x):   about 6 degree width
A 2 inch flash head at 9 feet (50x):   about 1 degree width
Our Sun (865,000 miles diameter, 107x):   0.5 degree size.
The trigonometry: degrees of angle = 2 arc tan(radius/distance)
``````

So, a one foot diameter light size placed 10 feet from the subject is seen by the subject as being 2 arc tan (0.5/10) = 5.7 degrees wide, or from 2.8 degrees either side.

But a four foot light placed 2 feet from subject is seen as 2 arc tan(2/2) = 90 degrees wide. So this light is also coming from 45 degrees either side of subject, above and below too, and so all those angular light rays are self-filling the shadows made by all the other paths, and are even wrapping around behind the subject in some degree. This is why "large" and "close" is the definition of soft light.

So just putting a diffuser on the small light is NOT at all the same thing as soft. Putting a diffuser on small light just scatters the light outward so that most of it misses the subject entirely. It has no diameter to angle any side light back towards the subject, to fill shadows made by other light paths.

So yes, inverse square law does affect the degree of light fall off behind and in front of subject. Greater distance does give less fall off. But greater distance is the absolute pits for softness.

If using tiny lights (bare flashes), softness can't matter, and 6 to 10 feet could have the fall off advantage you mention. A room may need a lot of depth, but a human portrait only needs about one foot, no big deal. Focus depth of field is surely more important.

But large lights at 6 to 10 feet is poor advice for portraits. The best rule for softboxes and umbrellas for portraits is "as close as possible" (meaning just far enough to keep them out of the camera view, barely). I'd say 4 or 5 feet ought to be easily possible for umbrella fabric, and 2 or 3 feet for softboxes. This makes these large lights appear huge... and soft.

Same size light as its distance is a good rule of thumb to provide decent softness. Four foot light at four feet works fine.

The main light is placed maybe 45 degrees high and wide, to intentionally make modeling shadows. These shadows can be pretty dark though.

So we use a fill light, which has to be frontal, to weakly illuminate and partially fill the shadows that the camera lens sees (and not make any more shadows). Lighting ratio is the ratio of these two light strengths (visibility of shadows remaining, some degree is desirable). But the fill light is frontal, and so has to be back near the camera so the camera can see around it. Above the camera is a good place for it. But it is just filling a few dark shadows, and because frontal is specifically NOT making any new shadows, soft is NOT its concern (no shadows to soften).

Overkilling this point, the fill light is close as possible to the lens axis, lighting exactly what the lens sees, so it makes no visible shadows needing fill. It merely lightens the existing main shadows that the lens sees.

The main light does need to be large and close and soft.

• Yes, the fabric plane becomes the light source. A difuse reflection becomes the light source. – Rafael May 11 '16 at 14:34
• I knew this would happen. :) If you measure from the actual flash tube, then inverse square law works very well (it simply must, since ISL is only about the similar triangle angles from the flash tube). But if you measure from the fabric, you are fooling yourself, and making it really difficult. You really should try this yourself to understand, but see scantips.com/lights/flashbasics.html#sb – WayneF May 11 '16 at 16:16
• Actually the same square law applies, but it has another mathematical variant which is the area, which provides a series of angular problems, which probably implies using integrals to solve, but again, the general square law applies. ;0) – Rafael May 11 '16 at 16:51
• A simple test. On a room where sunlight shines to a white wall, measure this incident light (the reflected one) And you see the drop with the distance... The light source is the wall, not the sun millions of miles away. – Rafael May 11 '16 at 16:54
• But I like your angular explanation. – Rafael May 11 '16 at 16:59