“As the circle of light increases, so does the circumference of darkness around it.” — Albert Einstein
I was fortunate enough to start in the lighting business when my own personal circumference of darkness was oh so small. I didn’t even know enough to know how little I knew. I was in the lighting business a long time before I stumbled across the secret to understanding the relationship between the five lighting metrics. It’s called ED-100.1.
“ED-100.1 Light & Color” is the first section in the Fundamental Level of the Illuminating Engineering Society of North America Lighting Education (www.iesna.org). The entire course is excellent, but if you do nothing else, read and understand pages 1-12 to 1-16 — the part that explains the five lighting metrics. You’ll learn in just a few minutes what it took me years to find out: The five lighting metrics hold the key to understanding all you need to know about lighting.
What are the five lighting metrics? They’re the fundamental ways that light can be measured and quantified. They tell us how much light a source produces in
total, how much light is falling on a surface area, how intense the light is in a certain direction, how much light is bouncing off of a surface and how much light is reflected and transmitted through a surface. In lighting terms, these are known as luminous flux, illuminance, luminous intensity, luminance and luminous exitance. Before you turn the page, give me five or ten minutes to illustrate these seemingly complex, yet rather simple concepts.
Luminous flux is simply the rate of flow of light. The yardstick that we use to measure it is called a lumen. If it helps you visualize the concept, you can think of light as a flow of particles. Then the light flux, or luminous rate of flow would be the total number of particles emanating from a source at any one time. It’s a bit more complicated that our simplified visualization of “particles” of light, but we’ll leave that in the circumference of darkness for the time being.
Now imagine that those tiny little particles of light are projected against a wall. If they all hit the wall within a very small area, then that area would be lit up very brightly. If, on the other hand, they spread out across a very large wall, then it wouldn’t be as bright. How many light “particles” fall in one area determines the brightness in that area. That’s called the illuminance, and we measure it in footcandles or lux, depending on which side of the Atlantic Ocean we reside. In numerical terms: The illuminance is equal to the luminous flux divided by the area.
The force with which our imaginary particles of light are leaving the source is the luminous intensity. It’s much like the water pressure in a hydraulic system or the voltage in an electrical system, except in lighting terms, the intensity can vary according to the direction we’re looking at. If we think of a typical household light bulb, the base blocks the light in that direction, so the luminous intensity is zero. That’s an example of its directional dependency. Luminous flux is measured in candelas, and one candela is defined as a source that produces one lumen at a one-square-foot spherical surface one foot away from the source.
Let’s keep our imaginations fired up for this one. Suppose now that the stream of particles emanating from our lamp source is as sharp as a laser beam. In fact, let’s imagine that they are traveling in a perfectly parallel beam, neither converging or diverging. That means we could measure the illuminance one meter from the source or 384 million meters from the source on the surface of the moon, and it would read the same (except for the light that bounces off of the particles in the earth’s atmosphere and in space). But in real life, the lights we use typically diverge, and the light spreads out as it travels. How much it spreads out, of course, depends on the distance it travels and the angle of divergence.
Suppose we have a source with a luminous intensity of 100 candelas. At one foot away from the source, if all the light falls on a one-foot-square surface, then it is producing 100 lumens, by definition, at that surface. Therefore, the illuminance is 100 footcandles (illuminance = luminous flux ÷ area).
If we double the throw distance, then the area will increase by a factor of four. Why? Because the area of a circle is pi (ï° or 3.14) times the square of the radius. If we double the throw distance, then the radius doubles; consequently, by squaring it, the area becomes four times as large.
Looking at our relationship between illuminance and area, we can see that the illuminance falls off exponentially in relation to the area and the throw distance. If we put all of this together, we can get to this relationship:
illuminance = luminous intensity ÷ (distance)2
That little line is what’s known as the inverse square law, and it says that the illuminance drops off exponentially with the square of the throw distance, but it’s directly proportional to the intensity. It’s an important relationship that will explain lots of lighting phenomena.
There’s one more little observation that ties all of this together. The area of a sphere is four times pi times the square of the radius of the sphere (4 x ï° x r2). So if a sphere has a radius of one foot, then the area is four times pi, or 12.6 square feet. Then a 100 candela source at the center of that one-foot sphere would produce 100 footcandles at the sphere. Since we know that the illuminance is equal to the luminous flux divided by the area, we also know that the luminous flux is the illuminance times the area. So we can calculate that the luminous flux from that 100 candela source is 100 times 12.6, or 1,260 lumens. So if 100 candelas is 1,260 lumens, then one candela is 12.6 lumens. Therefore, when we’re given the luminous intensity, we can convert it to luminous flux and vice versa.
Now that we better understand these lighting metrics, we can turn our attention to the light “particles” that we have been imagining. It turns out that light behaves as both a particle and a wave. If that’s difficult to understand, then you can better appreciate Einstein’s comment about the circumfer-ence of darkness. In other words, the more you know, the more you understand that there is even more to know and understand.
Whether this article increases your circle of light or leaves you in the dark, e-mail the author and let him know. rcadena@plsn.com.
