SI Units Explained with Worked Examples






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  Luminous intensity

How much brighter is a flashlight than a candle? Clearly it depends on how powerful the flashlight is, but there are other factors too. For example, the candle spreads its light in all directions whereas the flashlight is highly directional. This makes direct comparisons a little tricky, but not impossible. This is where the SI quantity of luminous intensity is useful. It has the SI unit candela and the symbol cd.

How many candles are as bright as a flashlight?

For much of history the candle was used as a measure of the intensity of light. This made sense in a world without light bulbs or other forms of artificial light, even if each country tended to use a slightly different kind of candle as its "standard". Things started to get complicated not just with the invention of light bulbs, but also with a greater understanding of the different colors of light. For example, the Sun's light is composed of all of the different colors mixed together, but, as seen from space, is faintly yellow in color, meaning that it shines slightly more brightly in yellow than the other color components.

For these and other reasons a better definition of luminous intensity was needed. The modern SI quantity of luminous intensity takes into account the color of the light and its direction. It is based on a frequency (light color) of 540 x 1012 cycles per second (hertz), which is roughly yellowish-green and is a color that the human eye is highly sensitive to.

Now the surprisingly easy bit. One candela is exactly equivalent to one candlepower (I did say it was easy!). So why is comparing a candle and flashlight tricky? To answer this we need to consider how the light spreads out from its source as well as taking into account a derived quantity called lumens.

Candlepower and candela are both measurements of light at source, but neither tells us how powerful the light is some distance away from the source. Instead, we measure the amount of light illuminating a surface area, which is called, naturally enough, the illuminance. The result is measured in lumens, with 1 lumen = 1 candela x steradian. For our purposes here we can think of the the latter term as an area, as the following example illustrates:

Imagine a transparent 1 metre radius sphere surrounding a candle. Its surface area will be given by 4 pi r2, so the surface area of our sphere is:

4 pi 12 = 12.57 m2

The amount of energy passing through 1 square metre of the transparent sphere is 1 lumen, and so it follows that 1 candlepower is 12.57 lumens. Many bulbs are now rated by the amount of illumination given at a distance. In SI units the standard is 1 lumen per square metre and called 1 lux.

Now let's return to flashlights, most of which are designed to be highly directional. If we have a 1 candela (i.e. candlepower) flashlight which just happens to have a beam that illuminates 1 square metre from 1 metre distance then that square metre will have an illumination of 12.57 lumens, as compared with 1 lumen for the candle. This is why it's not straightforward to compare the output of a flashlight with a candle. In short, when we want to measure how powerful a light source is we need to consider its nature or purpose - a half candlepower flashlight will be more useful than a candle for finding something in the distance at night. In this case the candle has more candlepower (i.e. a high candela rating) at its source, but the flashlight's light is focused and so more useful.

Finally, to put things into perspective, it's worth noting that a full moon on a clear night results in the Earth being illuminated by about a quarter of 1 lux at the Earth's surface. In comparison a typical living room will have an illumination of about 50 lux and direct sunlight results in anything up to about 130,000 lux at the Earth's surface.

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