Inverse Square Again

I've written about the Inverse Square Law before. But I  wanted to give a little different perspective on the Inverse Square Law here by adding a crude little video I just created with an iPhone, a white board, an LED flashlight, and some sticky notes. Let's start out with a description from Wikipedia:

In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.

The first thing to keep in mind is that strictly speaking, the law applies to light emanating from a point source. Most any photographic light we might use is much larger than a point source, so exact meter readings aren't going to happen. Where the law says that if you double the distance between the light and the subject the light will be 1/4 power, in practice it will be brighter than you expect. So please don't run off and set up a softbox, umbrella, or octabank and measure with your meter and come back saying it doesn't work. Please refer to the Wikipedia section on photography for more info.

What is more important here is the concept. Know that the closer your light is to the subject the faster it will fall off. As you move the light away from your subject, the slower it falls off. In practical situations, move your light in close to your subject if you want the background to go dark. Move the light further away if you need to even out the light (for example you want to have the background lit up or you have a group of people who are not all on the same plane with the light source).

You can almost think of light fall off similarly to depth of field. When you are in close on your subject, with high magnification, the depth of field falls off quickly. Only a small part of the scene is in focus. With the light in close, just a small part of the scene is lit and the brightness falls of quickly. When you are further away from your subject the depth of field is greater. When the light is further away, the intensity is more constant/even through the frame.

I think there is still some confusion about why light falls off so quickly. What is happening is that as the light photos stream away from the light source, they spread out in a cone-shaped pattern. The light doesn't really get dimmer, but the photons have to spread out further to cover the area of the cone pattern as they move away from the source of the light. As they move away the rays start to get more parallel and at that point the falloff stops happening. To show that the light is not getting dimmer, think of a city skyline in the distance. You can see the lights in the windows of the buildings when you are miles away. But there isn't any chance that those lights are illuminating you when you are at a distance. Same thing with an airplane flying overhead at night. You can easily see the marker lights on the plane at their point of origin, but they are too spread out by the time they actually reach you to have any effect on lighting you.

Think of the sun and earth. If we were able to be close to the sun the light skimming across the planet would be much brighter on one side than the other. But due to the distance between the sun and earth the light rays from the sun are reaching us in a parallel fashion. The light on the top of a mountain is the same intensity as at the base of the mountain if there is nothing blocking the light and causing shadows. When you stand on a beach and look out to the horizon, the brightness remains constant. You can see a ship off on the horizon many miles away. It doesn't fade into darkness until the sun goes down. The same amount of light hits the sand where you are standing as hits the ship on the horizon.

Here is the video:

For this demo I've set up a small LED flashlight as the light source. It is not a point source, but I think it should do for the demonstration. 

At first I have it set at 6 inches from the whiteboard and I have drawn a circle around the light hitting the board. Next. I moved the light back to 12 inches and drew another circle. This should start making things click if they haven't already. Note that the light expanded in all directions when I moved it back.

Then I added another element--sticky notes. I have one here that is approximately the size of the original circle that I used to cover that inner circle. How many sheets of paper will we need to cover the larger circle caused by doubling the distance of the light to the white board? At first you may be tempted to answer TWO. Seems reasonable. Double the distance equals twice the size. But that is incorrect. The light beam is expanding in all directions, so to cover the second circle I needed 4 pieces of paper. The light has spread out so that is is 1/4 the intensity at twice the distance. If I doubled the distance again so the light was four times the distance, it would take 16 pieces of paper to cover the circle.

I hope that this gives a little clearer demonstration of what is happening to the light beam as it expands as it gets further and further away from its source.

Here are a few more links with photographic demonstrations… This Week in Photo; Mark Wallace's YouTube video; and WikiPedia.

Round or Square?

Catchlights that is.

Catchlights are those highlights that give life to your subjects' eyes in your photographs. Without a catchlight, the eyes can look lifeless. So much so, that in the old days of glamor and hollywood portraits they would paint in catch lights if the lighting setup didn't provide them.

Every once in a while I get into a discussion with other photographers about catch lights. Some people like round ones. Others like rectangular. I fall into the "rectangle" camp and would like to offer my reasons. I also like LARGE round catchlights, such as from a large octabank. See my next post for more about that.

When I think of catchlights, I think of old masters paintings. And I think of light coming from a window or a doorway. And in most situations, those windows and doorways are rectangular. But what about the great outdoors? The catchlight in the great outdoors is often provided by the full sky. And that tends to be rectangular in shape.

Other folks say that the catchlight should be round. They say the main source of light in the world is the sun, and the sun is round. I don't disagree, the sun is pretty much round. But the sun rarely provides a catch light. For one thing, it is so far away that if it does show in the eye, it is just a pin-point. And if the sun is shining directly into the subject's eyes, their probably squinting and not looking all that comfortable, and the squint may be blocking the catchlight. Or it is so bright that the subject looks away from the sun, and now the wide open sky provides the light for the scene and the catchlight.

So, there's my argument. But, as with all things, it doesn't matter what I think. It doesn't matter what other photographers think, either. It just matters what you think. You like round catchlights? Use round lights or modifiers and be happy. You like rectangles? Use rectangular lights or modifiers and be happy.

All I ask is that you think about it and reason out why you have one preference over another. And maybe you don't have a preference. That's OK, too.

And now you get to look at my pretty face (that's what happens when the model has to cancel at the last minute)...

 

This first image was created with a Photoflex Silverdome NXT Medium Softbox. Below is a close up crop of my eye from the above photo.

 

 

This second photo was taken using a Speedotron 22" beauty dish with a diffuser on it. Below is the close up crop.

 

 

This third image goes back to the Photoflex softbox, but I added three strips of black tape across the face of the softbox to try to imitate the look of a window. Again, below is the close up crop.

What is your preference for the shape of a catchlight? And what do you think of multiple catch lights, as you might get from some multiple light studio setups? The above photos were all made with one light and no fill, so only show the single catchlight in each eye. A reflector board or secondary fill light may have added an additional reflection in the eye.

 

For this image, I kept with the Photoflex softbox, but added both a white card and a Photoflex 32" 5-in-1 MultiDisk reflector with the gold covering, which provided an extra reflection in the eyes (as well as a warmer overall tone to the image). In this case, I don't think it detracted. But if the extra reflections were harder and more similar to the main catchlight I would suggest removing the extra catchlights in retouching.

 

Speaking about catchlights and portrait lighting, the catchlight is what we call a specular reflection. It reflects the light back to the camera like a mirror. And like a mirror, the brightness will remain the same, no matter the distance between the light and the subject. At first, this seems to contradict the inverse square law, but it actually doesn't. The inverse square law says that when you change the distance between the light and subject, the amount of light will change by the square of the change. So, if you moved your light from 2' to 4' from the subject (2x the original distance), the subject would receive 1/4 the amount of light. If you moved the light 3x the distance, the subject would receive 1/9 the amount of light.

In the case of a mirror reflection, instead of the brightness changing, the size of the light will change. So if you move the light twice as far back, instead of the light falling off to 1/4 power, the size of the light in the eye would be 1/4 the size, but at the same brightness. Knowing this, we can control the brightness of the catch light. To make it darker in the overall exposure, you would have to bring the light in CLOSER. By bringing it closer, the catchlight gets bigger, but remains the same brightness. However, by bringing the light in closer the overall scene (the face) gets brighter. And you have to lower the exposure (stop down the lens or lower the power of the strobe) to get the proper overall exposure, and by doing so, you are also darkening the specular reflection, bringing closer to the overall exposure level.

Remember to check my follow up post about larger catchlights.

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All images taken with a Canon 5DmkII and Canon 70-200L f/4 IS lens. Manual white balance setting of 5700 degrees Kelvin was set in the camera. Light was a Speedotron Force 5 monolight that remained the same spot for all images (just the modifier was changed between the softbox and the beauty dish. With a little bit of work the Speedotron beauty dish can be modified to fit onto other strobes, but you are on your own for that. At around $150, this beauty dish is a bargain.