Greenwood press
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book-20600
46
INVERSE FUNCTION INVERSE SQUARE FUNCTION The inverse square law explains why sound drops off so quickly as you move away from a source of noise, why porch lights do a good job of illuminating the front of a house but not the street in front of the house, and why the forest reverts to darkness as you move away from a campfire. Light and sound emerging from single sources can be viewed as increasing spheres whose area increases as the square of the distance from the source. As a result, the proportion of sound or light reaching a specific unit of area, such as a square meter, varies inversely as the square of the distance from the source. The standard equation of an inverse square function is y = k x 2 , where k is a constant of proportionality. Light emerges from a source in all directions. The drawing below illustrates the distribution of light from a 40-watt light bulb. We will use wattage as the measure of pointance and illuminance to show how the inverse square works. Imagine a sphere of radius r containing the light bulb. Forty watts fall on the interior surface of the sphere. The surface area of the sphere is given by SA = 4πr 2 square meters. The energy falling on 1 square meter is therefore 40 watts divided by 4πr 2 . In the drawing, this energy is called “L.” If you go out twice as far, the same energy is distributed over 4 square meters. At three times the dis- tance, the energy is distributed over 9 square meters. A standard formula for light intensity is E = I r 2 , where E is called the illu- minance, and I is called the pointance. Illuminance is measured in a variety of units such as lux and footcandles. Pointance is a measure of the intensity at the source of the light. As you can see, this is a direct statement of the inverse square law. The inverse square law provides information about the likelihood of other planets having life forms similar to those on earth. Imagine the light that hits your Download 1.81 Mb. Do'stlaringiz bilan baham: |
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