Found this response on photo.net from someone asking about using 3 strobes to light a subject. Probably the most technical explanation ever that actually makes sense. For those of you who know a lot more about lighting than I do, please post if the following response is valid or if the person is talking out of their rear.
Alan Marcus 
, Jun 29, 2009; 01:28 p.m.
"In
photography the lighting ratio is the key resource we have to control contrast. Consider; our media is two dimensional (except for specialized cases), thus we must create the illusion of depth with our lighting otherwise the picture appear flat. Consider an aerial photo of a telephone pole. From above it’s not much to look at. Shoot with a morning or evening sun and the elongated shadows produce an impression of depth and elevation.
Portraiture is the study of the human head, a round figure scattered with projections and valleys. We light to give an illusion of depth. Additionally most believe we should preserve an illusion that just one light was used (comes from a study of the master working in oil on canvas), if multiple directional shadows are detected, the picture will look weird. So we light using a main
light fixture
set high to simulate midday sun. We position the main in such a way that the shadows that result enhance features. Long nose; light with short nose shadow. Short nose; light with long nose shadow. Oval face; light from the front, to make the face appear more rounded. Fat face; light from the side, keeping the opposing cheek in shadow to give an illusion of a thinner face. Positioning the main is an acquired skill.
Now for contrast control: Both film and digital lack the dynamic range of the human eye/brain. When taking a picture we see detail in the shadows that the camera is unable to record. Thus for fine portraiture, we are forced to diminish shadows, this translates to filling them with light. Otherwise the shadows record void of detail. You are advised to fill shadows from the camera’s prospective. This is accomplished by positioning the fill lamp somewhere along an imaginary line drawn between camera and subject. Its elevation is set to lens height. OK if fill strays off this line as needed to prevent the fill fixture from getting in the picture.
We start with a two lamp set-up
Consider a portrait 2:1 (Flat Lighting)
We place the main high and off to the side causing it to shine down on the subject. Let’s say the main delivers 1000 units (watts if you like) on the subject. The fill is placed near lens axis and adjusted to deliver light to arrive at the subject plane with equal light energy as the main. Thus the main and the fill each contribute 1000 units of light. Now the frontal part of the face receives light from both. Thus the total on the frontal areas of the face will be 2000 units. Now some areas of the face are in shadow. These are locations where the main could not reach, we are talking about dimples and valleys and nose shadow etc. Consider the circumstances; 2000 units on the frontal areas and 1000 units in shadow areas. Mathematically this can be stated as a ratio. The ration is written as 2000:1000. This is handled like a fraction that van be reduced by dividing both sides by same number; in this case 1000. The reduced ratio is written as 2:1. This 2:1 lighting ratio is flat nearly featureless.
Now consider a portrait set-up 3:1 ratio (bread and butter lighting). This is the one that wins contests and sells best. To achieve we reduce the fill energy at the subject plane to ˝ power as compared to the main. We might do this by setting, a knob on the fill lamp or we can just move the fill fixture further away from the subject.
We can calculate the fill-to-subject distance (assumes both main and fill are identical). We measure main-to-subject distance and multiply this value by 1.4. The answer is a revised fill to subject distance. This added distance reduces the light energy playing on the subject by 50% (1 f/stop). The 1.4 factor is derived from a law in physics known as the inverse square law. The idea is to cause the main to deliver 1000 units and the fill 500 units. Now consider the frontal area of the face get light from both fixtures. The values are 1000 main + 500 fill. Thus the frontal areas receive 1000 + 500 or 1500 units. Shadows receive only the fill’s 500. Ratio is 150:50 reduces to 3:1. This is achieved if the fill is subordinate to the main by 1 f/stop. You can also place main and fill using a meter. The trick is again 1 f/stop difference, fill subordinate.
Consider 5:1 somewhat more zippy lighting.
We reduce the fill to 1/4 power by knob on the unit if available or by setting the fill even further back. If the fill is at the 2:1 distance (same distance as main) we multiply by fill-to-subject distance by 2. If the fill is positioned at the 3:1 distance, multiply fill-to-subject distant by 1.4. You are after a two stop difference with the fill subordinate to the main. How is this 5:1? This placement causes the fill to be 2 f/stops subordinate or 25% of the main’s energy. Now the frontal area receives 1000 from the main and 250 from the fill for a total of 1250 frontal and 250 in the shadows. The ratio is 1250:250 or 5:1. This is contrasty lighting.
Consider 9:1 somewhat theatrical, very zippy lighting.
If we reduce the fill to 1/8 power by knob or measurement 3 f/stops subordinate to the main. From the 2:1 position the multiplier is 2.8 from the 3:1 position the multiplier 2, from the 5:1 position the multiplier is 1.4. Main continues to delivers 1000 units the fill 125 units. Thus the frontal areas receive 1125 the shadows 125. The ratio is 1125:125 = 9:1 This is a 9:1 exceedingly contrastry lighting considered theatrical. Note 9:1 is the maximum ratio. Any more reduction and the shadows will be void of detail.
To review:
Main at 4 feet fill at 4 feet ratio is 2:1
Main at 4 feet fill at 5.6 feet ratio is 3:1
Main at 4 feet fill at 8 feet ratio is 5:1
Main at 4 feet fill at 11 feet ratio is 9:1
The third lamp can be used to illuminate the background. It is placed low behind the subject aimed up at the background. Its distance to background determines the apparent density of the background. It can be made to appear white of gray or black. Lamp-to background distance also obeys the 1.4 factor method or knob settings or metering.
It is no accident that the lamp-to-subject distances follow the f/number set which is 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22.
Note each value going right is its neighbor times 1.4.
Each value going left is its neighbor divided by 1.4
I call this kind of math gobbledygook"