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
Euan S.
Jul 12, 2016

45 foot-candles.

Explanation:

#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.

#color(blue)("Method 1")#

#I_1 = k/d_1^2 implies k = Id^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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