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Inverse Proportionality
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Priyaranjan
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Q. The "luminous flux", or perceived brightness, of a light source is measured in lumens and is inversely proportional to the square of the distance from the light. If a light source produces 200 lumens at a distance of 3 meters, at what distance will the light source produce a luminous flux of 25 lumens?
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Matt@VeritasPrep
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Inverse proportion says
x * y = some constant, for the two variables x and y. (We don't need to know what this constant is, as we'll see below; we just need to know that it doesn't change.)
In our case, x = lumens and y² = distance.
In the first case, x = 200 and y = 3.
In the second case, x = 25, and y = unknown.
Since they have to equal the same constant, given that they have the same inverse ratio, our equation is
200 * 3² = 25 * (distance we want)²
This gives
(Distance we want)² = 72, or
Distance we want = √72 = 6√2
x * y = some constant, for the two variables x and y. (We don't need to know what this constant is, as we'll see below; we just need to know that it doesn't change.)
In our case, x = lumens and y² = distance.
In the first case, x = 200 and y = 3.
In the second case, x = 25, and y = unknown.
Since they have to equal the same constant, given that they have the same inverse ratio, our equation is
200 * 3² = 25 * (distance we want)²
This gives
(Distance we want)² = 72, or
Distance we want = √72 = 6√2
