# 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?

Apr 25, 2016

#### Answer:

Light intensity at 2 feet is 8 lumens

#### Explanation:

Let intensity be $i$

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

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

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Given condition$\to i = 8 \text{ at } d = 3$

$\implies 8 = \frac{k}{{3}^{2}}$

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

$\implies 8 \times {3}^{2} = \frac{k}{\cancel{{3}^{2}}} \times \cancel{{3}^{2}} = 72$

Then: $i = \frac{72}{d} ^ 2$
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So at 2 feet we have: $i = \frac{72}{2} ^ 2 = 18$