Yes and no. Unlike, say, a sound wave, visible light is electromagnetic radiation which only acts 'wave like'. There is a calculus method of determining more precise "electromagnetic intensity", but your formula is roughly correct.
However, in visible light we don't normally talk about electromagnetic intensity, but "Luminous Intensity", which is quite a bit different. A standard unit for Luminous Intensity in photometry is the Candela. Defined as:
One steradian is an angle whose vertex is at the center of a sphere and that is subtended by a surface area equal to the radius squared (picture a tiny flashlight shining out from the center of a frosted globe).
For practical purposes we usually go one step further and convert Candela (Iv) to a specific luminous flux at a planar point, like Lux (Ev).
I'm sorry, I don't know any good online references off the top of my head, but I can look around if you are interested.
Choosing the right Stage Lighting Instruments: (Bulbtronics Which to Use? Pamphlet by Glen Cunningham for Bulbtronics 1998)
Beam Distribution Basic Terms: When you look at the total area of light, or “field,” projected by a stage lighting instrument you realize there are only a few basic variables: the magnitude of the center of the beam intensity; the distribution of intensities throughout the entire field; the field’s focus; the character of shadows the field creates; the angle of spread; the shape of the field; the color temperature; and the response to control.
The Magnitude of the Center Beam indicates how intense a field an instrument projects. This, in turn, determines the brightness of an area on which it is projected of an area on which it is projected at any given throw distance. For your design, you must match the candlepower of the instrument (measured in candela) to the brightness you wish to have in the area it will light. The higher the candlepower, the brighter the light. The brightness is determined by dividing the candlepower by the square of the throw distance.
The Distribution of Intensities refers to the candlepower, or amount of light at every point within the field. Mathematically speaking, it’s a distribution curve with the candlepower as the Y factor of a line graph and the degrees or distance away from the center beam as the X factor of the graph. Distribution curves very greatly, ranging from a very flat filed with fairly equal intensities across the field, to a very highly-peaked field with a very intense center and a rapid drop-off away from center. Some popular field distributions resemble a classic bell-type curve with a bright center and a gradual decline in intensity toward the outside.
No curve is better than another, since each play a part in your design that another may not fill. “I remember using a 6" fresnel with its lens removed and its reflector beaten up for one effect on a show. By purist standards the field was horrendous - inefficient, uneven, and harsh, among other things - but it created the desired effect better than any other instrument.”
A flat field is better for projecting silhouette patterns and slides, and when you use a single spot to light an area. Choose a highly-peaked field for lighting a relatively small, specific area (a “special.”) The bell-type curves are best for blending instruments to create a wash some fields are asymmetric, throwing more light away from a reference line (normally a horizontal line through the lamp, running parallel to the stage floor) than near it. This is useful for creating even cyclorama effects. You always can make compromises between distribution types, using for instance flatter bell-type curve for both projecting and blending a wash, and a more peaked bell-type curve for both projecting and blending a wash. There are no hard-and-fast rules, however. “I have used a very peaked field to great effect for gobo projection.
Field Focus is either hard or soft. A hard focus will produce a well-defined projected image of anything at its focal point and hard edges. A soft focus will project a poorly-defined image and the field edges will have a soft, fading quality to them. You use a hard focus when you want to project the image of either a silhouette pattern (gobo), including the round gate of an instrument for a hard spot, or when sharp, defined shutter cuts are desired.
A Softer focus is better for lighting that is supposed to blend, and not supposed to indicate the direction of the source. It also can be used when projecting a pattern to create texture with soft shadows. A soft-focus instrument also will cast softer shadows on or behind objects it shines on - particularly useful when too many hard shadows make the scene too busy, change its character, or break its realism. “I often have used a break-up patterngobo with a soft focus to create the illusion of light shining through trees.”
The Angle of Spread defines how much of the stage a single instrument can cover. All instruments have a beam angle and a field angle. The beam angle is where you measure 50% of the center beam candlepower (cbcp). The field angle is where you measure 10% of the cbcp. A spot or special will want a smaller angle to help isolate it from other areas on stage, a wash will benefit from wider angle instruments, using fewer to wash the entire stage. The beam angle often is used to determine on-center distances for blending a wash.
Field Shapes vary greatly. Most are round, but some are square, oval, and rectangular. Color Temperature is specific to the lamp used in an instrument. The higher the color temperature, measured in degrees Kelvin, the “whiter” the light is said to be. And the whiter the light is said to be. And the whiter the light the brighter it appears to be. So, using two instruments with color temperatures that differ greatly can create a bold contrast, or ruin an even wash, depending on the circumstance. Higher color temperature fields also project more vivid colors when gelled and so are good for bold colors washes and specials.
Response to Control refers to the rate at which the instrument (and thus the field) changes when prompted. Some instruments, particularly those with large, heavy filaments, lag a great deal from the time a cue is executed to the time it actually finishes. This is a particular problem if the lag is much slower than the cue as you have designed it. A sharp blackout is impossible if the stage is washed with instruments whose fields are going to dim slowly down to black. In those cases, the best you may get is a fast fade to black. The same problem occurs when you want to flash, chase, or strobe a bank of instruments. The slow burn-down can kill the effect entirely.
Building your Lighting Sense: These field characteristics are the tone and timber of the light you will use to render your design. To those you add some of the instruments’ general mechanical abilities, such as shutter cutting, barn-dooring, adjusting from a hard to soft focus, or narrow to wide spread. And, of course, each instrument type provides you with its own unique capabilities. See table below for some of the field characteristics and mechanical abilities of the more common instrument types. However, you will learn a great deal more about the character of the light projected by your instruments if you run some tests. Set up one of each of the instrument types you have available, focusing them on an area representing a stage with some furniture and people or objects. Be sure to choose instruments representative of those you will be using. If you don’t have access to the stage itself, any area will do as long as you can get far enough away to look at the area being lit to see what the light actually does.
However, don’t just shine an instrument onto a flat wall and look at it. That’s not going to reproduce the conditions under which you will use it. You will be using equipment focused on varied surface textures and with many different objects on stage. The effect the light has on the atmosphere under those conditions is completely different than when you shoot it straight at a wall. And remember, creating with light is like painting with broad strokes, not drawing with fine lines. Look at the overall field and the feel it offers.
When you have the instruments set up ( start off without any color,) carefully consider what you see the light doing. Look at the surfaces and objects that are being lit. Are there hard or soft shadows? Is a large or small area covered? Is there a hard or soft edge to the beam? If the instrument has some kind of shuttering or barn doors, are the cuts well defined or diffuse? Does the light punch through with an obvious indication of where the light source is, or does it create a more general illumination, with less obvious directional quality to the field? What happens when the field is dimmed? Write down your observations - they’ll be useful as you lay out a design.
If time and space allow, experiment by using pairs of instruments together - of the same type and different. See how their fields complement or contrast each other. How well do they blend or combine? This will be valuable time spent building an understanding of how to create the visions you wish to put on stage. If you have never taken the opportunity to do this, regardless of how long you’ve used your equipment, try it. You may be surprised with some the characteristics you never noticed about the light that each instrument type delivers.
Now look at each wash, special, and effect in your design, and write down any characteristics of light that would help them. Try to keep your descriptions brief, using single works like “hard,” sharp,” intense,” and “shuttered” when possible. When you’re finished, compare the list with the characteristics and capabilities of the instruments you have to work with. Look for the instrument type that delivers the most characteristics for each effect.
Sometimes you may find you don’t have enough instruments to fill every need, or even enough to go around. If you’ve gone through the process above, however, you can make intelligent compromises by deciding which characteristics are most important for each effect and reserving the appropriate instruments for those effects, and getting the most out of the rest.
When you know what you want from an instrument - and what you can expect from it - you can make more informed choices and compromises so your design works the best it possibly can using the tools available to you.
EllipsoidalReflector Spotlights: (Lekos) are usually specked out as 6x9, 6x16, 30 degree, mini-ellipse etc, or brand name like 29° Source Four or “Berkly” Also called patternunit, and spot light. Fixed focus and zoom units are available.
units with an ellipsoid shaped reflector, lenses in the front and framing shutters in between. The front lenses are mounted in a movable “barrel” or lens train. The barrel allows the focus to change from sharp to moderately soft. Zoom units have a variable size beam, which is adjusted by moving the lenses closer or further away from each other, as well as for fixed units by adjusting the focus some by moving the lens train distance from the reflector shorter or longer.
4.5x6 fixtures are 50° beam spread. 6x9 = 40°, 6x12 = 30°, 6x16 = 20° and 6x22 = 12° in general these focal length and diameters are standard. All but the 6x16 is made up of two lenses, the 6x16 is made up of a single 6x22 lens. As the focal length of the instrument goes up, so does the distance the lens must be from the reflector, also the amount of magnification in the lens goes down. with focal length increases.
Fresnels are specked by lens diameter, wattage, or model. Eg. as 6", 8", inky, duce, 5K, tener. The unit has a spheroid shaped reflector and fresnellens in front. The reflector and lamp move back and forward together inside the unit to provide a variable size beam. The focus is always soft, and beam shape can be affected by barn doors and snoots (top Hats).
Scoops are specked by wattage and size. They are also called flood lights, ellipsoidalreflector floods. the reflectors are large and elliptical sometimes used with a frosted lamp and no lens. It is used for soft even lighting of a large area usually a cyc or backdrop. Cyc Units are specked by wattage and number of cells also called a far cyc or Ianiro. These fixtures are open faced that use a linear filament lamp and irregular reflector to light a cyc or backdrop evenly from top to bottom. Usually wired for 3 or 4 color cells per unit.
Strip Lights specked out by lamp type and wattage, length, and number of circuits or lamps. Used primarily for lighting drops or overall stage toning, these units have a series of lamps wired to work in sets of 3 or 4 circuits. Lamps available include MR16, Par38, R40, Par56, Par64 & T-3 lamps from 50 to 1,000 watts.
Follow Spots: A high intensityfixture that is generally used to highlight a single performer. and operator is required. Units range from small incandescent units for small stages, to large HTI or Xenon (arc) lamps for arenas. Color changers are internal and can be customized. Most units have iris and zoom capabilities. Appropriate units are chosen by the throw distance, and overall light levels on stage. Designlab Chicago Rental Catalog 1.0 (1992) pp.6-10
Lenses - Focal Points: The relationship between the positions of the light source or the object (slide,) and the point where the transmitted rays from an image is determined by the “Lens Formula.” When P = the distance from the object to the principal plane of the lens, Q = The distance from the principal plane to the image, and F = The focal length of the lens; than 1/P+1/Q=1/F.
Focus of Focal Center: when the source (given the lamp is out of focus with its reflector,) is moved forward from the principal focus, the reflected rays converge. When moved back from the principal focus, they diverge with a dark spot in the center of the beam. Also a bright half or partial moon like figure hanging around the center of the beam, denotes a lamp horizontally out of focus with the reflector and its lenses in the opposite direction as is shown
The fundamental units of these concepts would be useful, and will aid in proper multiplication and division of the units. For example, feet and meters are length, L; area is LxL. Flux must have a time component T (in the denominator). I’m hung up on the lumen and candle basic units, although a reference that I have says that the lumens and watts are both units of power.
Also, two of the equations are:
Foot-candles = candela / distance in feet * distance in feet
Lux = candela / distance in meters * distance in meters
Should these be:
Foot-candles = candela / (distance in feet * distance in feet)
Lux = candela / (distance in meters * distance in meters)
Generated luminous flux (lm)
- are F and lm identical?
[Finally - one equation reads:
Lambert * 295.720 = candles sq. ft. should probably be… candles / sq. ft]
Also, this sounds like another area where technical terms are misused by laymen. (like in the case of pipe diameters.)
My notes are directly out of the manufacturer catalogs but I will update with what you cite. I believe you are correct in the Foot-Candle and Lux figures. Believe I did miss a / in the Lambart also. Thanks.
Luminous Flux Ф = a unit of measurement: Lumen (lm). All the radiated power emitted by a light source and perceived by the eye is called luminous flux. - Osram Photo-Optic Lighting Products, 1999 Flux by the specs can be either initial or mean - normally initial after burn in time is used because most stage and studio lamps are known to maintain initial output thru the life of the lamp. Or at least it’s a figure more provided amongst all brands for comparision.
Cand. = Candlepower, Candlepower is the normal rating method of the total light output of miniature lamps. To convert this rating to lumens multiply it by 12.57 (4 pi).
Mean sphericalcandlepower MSCP is the initial mean candlepower at the design voltage. It is subject to manufacturing tolerances. Mean sphericalcandlepower is the generally accepted method of rating the total light output of miniature lamps.
cd = Candela. The international unit (SI) of luminous intensity. The term has been retained from the early days of lighting when a standard candle of a fixed size and composition was used as a basis for evaluating the intensity of other light sources.
A few more notes of interest on the subject in question:
Luminous Intensity I = Unit of measurement: candela (cd). Generally speaking, a light source emits its luminous flux in different directions and a different intensities. The visible radiant intensity in a particular direction is called luminous intensity. - Osram Photo-Optic Lighting Products, 1999
Luminarie Efficiency = The ratio of total lumens emitted by a luminary to those emitted by the lamp or lamps used.
Luminarie efficiency (also known as light output ratio) is an important criterion in gauging the energy efficiency of a luminarie. This is the ratio between the luminous flux emitted by the luminarie and the luminous flux of the lamp (or lamps) installed in the luminarie. For detailed information on indoor lighting with artificial light, see DIN 5035. - Osram Photo-Optic Lighting Products, 1999
Voltage and Light Output: The effect of voltage on the light output of a lamp is ±1% voltage over the rated amount stamped on the lamp, gives 3.1/2% more light or Lumens output but decreases the life by 13% and vise a versa.
Do not operate quartz Projection lamps at over 110% of their design voltage as rupture might occur. GE Projection, Ibid p.13
A 5% change in the voltage applied to the lamp results in
-Halving or doubling the lamp life
-a 15% change in luminous flux
-an 8% change in power
-a 3% change in current
-a 2% change in color temperature (0.4% change per1% voltage.)
Osram Technology and Application Tungsten halogen Low Voltage Lamps Photo Optics, p21