The intensity of light received at a source varies inversely as the square of the distance from the source. A particular light has an intensity of 20 foot-candles at 15 feet. What is the lights intensity at 10 feet?

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The intensity of light received at a source varies inversely as the square of the distance from the source. A particular light has an intensity of 20 foot-candles at 15 feet. What is the lights intensity at 10 feet?

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Answer 1 · 2016-07-12T17:32:34

45 foot-candles.

Explanation:

$I \propto \frac{1}{d^{2}} \Rightarrow I = \frac{k}{d^{2}}$ $I prop 1/d^2 implies I = k/d^2$ where k is a proportionality constant.

We can solve this problem in two ways, either solving for k and subbing back in or by using ratios to eliminate k. In many common inverse square dependences k can be quite a lot of constants and ratios often save on calculation time. We will use both here though.

$Method 1$ $color(blue)("Method 1")$

$I_{1} = \frac{k}{d_{1}^{2}} \Rightarrow k = I d^{2}$ $I_1 = k/d_1^2 implies k = Id^2$

$k = 20 \cdot 15^{2} = 4500 foot-candles f t^{2}$ $k = 20*15^2 = 4500" foot-candles"ft^2$

$therefore I_2 = k/d_2^2$

$I_2 = 4500/(10^2)$ = 45 foot-candles.

$color(blue)("Method 2")$

$I_1 = k/d_1^2$

$I_2 = k/d_2^2$

$(I_2)/(I_1) = k/d_2^2*d_1^2/k$

$implies I_2=I_1*(d_1/d_2)^2$

$I_2 = 20*(15/10)^2 = 45 " foot-candles"$

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The intensity of light received at a source varies inversely as the square of the distance from the source. A particular light has an intensity of 20 foot-candles at 15 feet. What is the lights intensity at 10 feet?

1 Answer

Explanation:

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