The intensity of a light varies inversely as the square of the distance from the light source. If the intensity from a light source 3 feet away is 8 lumens, what is the intensity at a distance of 2 feet?

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Answer 1 · 2016-04-25T19:58:26

Light intensity at 2 feet is 8 lumens

Let intensity be $i$ $i$

Let the distance from light source be $d$ $d$
Let the constant of association be $k$ $k$

Then: $i = \frac{k}{d^{2}}$ $i=k/d^2$

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Given condition $\to i = 8 at d = 3$ $-> i=8" at "d=3$

$\Rightarrow 8 = \frac{k}{3^{2}}$ $=> 8=k/(3^2)$

Multiply both sides by $3^{2}$ $3^2$

$=> 8xx3^2=k/(cancel(3^2)) xxcancel(3^2) = 72$

Then: $i=72/d^2$
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So at 2 feet we have: $i=72/2^2 =18$