How to compare the brightness power measurement of a torch? ?

Watt gives the used electrical power which you have to pay, cd and lumen die light power. cd is used if the lamp does not work equal in all directions.

Pleas excuse my bad English.

Radiometric measurements of light use values like watts, watts per square meter, watts per steradian etc.. These are more likely used with sunlight where the number of watts is relevant, such as fo heating or solar panels, or for infrared or UV wavelengths that are not visible.

The SI base unit for photometric measurements of visible light is the candela, so other such units are based on this. Photometric measurements are weighted for the wavelength, according to the sensitivity of the human eye to different wavelengths. A blue or red light will be seen as less bright than a green light of the same power or brightness. The standard weighting curve is called the photopic curve (first link). At a specific green wavelength of ~555nm there are ~630 lumens per watt. There are 630 candela per watt per steradian. At any other wavelength on the curve more power is needed to look the same brightness. The old name for candela is candlepower.

This means a light source that radiates equally in all directions (isotropic) and has a luminance of one candela will have an output of 4 x pi lumens = 12.57 lumens (the surface of a sphere is 4pi steradians at any distance). The angles in spheres are called solid angles. How does that help?

The significance of a steradian is that the area on the surface of a sphere is r^2 per steradian. This means it is handy for determining the area at any distance, and so the brightness in lux, which is lumens per square meter. This also introduces the inverse distance squared law. The surface area for one steradian at a radius of 100mm is 10,000mm^2. Easy.

A candela takes into account the brightness in a particular direction, so is likely to be used with a torch. It gives huge numbers for marketing, if nothing else.

When a spot light has 1 million candle power, it means 1 million candela luminance in the beam. This means the power (in the beam only) is the equivalent of 1 million lumens per steradian. The beam can be compared with a steradian by measuring its area at a specified distance.

Lets say that at 100m the beam was 2m diameter. The cross sectional area is therefore 3.14m^2. At 100m the 1 steradian beam would have a surface area of r^2 = 10,000m^2, a much bigger area, and so the ratio is 10,000m^2 / 3.1414m^2 = 3183 times the spot beam area in this case.

Therefore the power from this lamp (remembering cd = lm/sr) in lumens is 1,000,000lm/sr x 1/3183sr = 314 lumens.

To get a feel for the power in watts, if it was a single green colour at 555nm wavelength, it would be 314/683 watts of light = 0.459W. If the lamp was 10% efficient overall, including the focusing system, it would have an electrical power of 45.9W. It can be seen how this relates to a 50W QI bulb, even ignoring the spectrum.

Many 12V x 50W spotlights are rated something like 1 million candelas. Leds are from milli-candelas up to about 15 candelas (for plastic 5mm type). As a green LED is ~560nm and so close to 555nm, it is relatively easy to convert to watts. Other colour LEDs are corrected by the weighting factor for the photopic curve (so have more power than at green). With white lamps, the spectrum has to be known, and integrated to the equivalent average of green. Not so easy.

A lumen is related to watts, and is therefore used to indicate the total luminous power (also called flux) from a lamp. It takes no account of the brightness in a particular direction or at a particular distance. In candela terms, one lumen is one candela-steradian. Conversely, a candela is one lumen per steradian.

A light meter is likely to measure illuminance (brightness) in lux. One lux is one lumen per square meter, so is a measure of the brightness from a lamp, at a table surface, etc. It is used for photography, and office lighting, etc. The example 1 million candle power lamp would measure 314 lumens per 3.1414 square meters, so it is 100 lux. More directly, 1 million cd @ 100m has an area of 10,000m^2, so 1,000,000 lumen / 10,000m^2 = 100 lumens per square meter = 100 lux.

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