The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 15 ft from the light.
A) $1 \frac { 2 } { 9 }$ foot-candles
B) $\frac { 2 } { 9 }$ foot-candle
C) $\frac { 1 } { 5 }$ foot-candle
D) 2 foot-candles

Question

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 15 ft from the light. 
A) $1 \frac { 2 } { 9 }$ foot-candles
B) $\frac { 2 } { 9 }$ foot-candle
C) $\frac { 1 } { 5 }$ foot-candle
D) 2 foot-candles

Quizplus · Accepted Answer

The intensity of light varies inversely as the square of the distance, so $I = \frac{k}{D^2}$, where $k$ is a constant. Given $I = 2$ foot-candles at $D = 5$ ft, we can find $k = 2 \times 5^2 = 50$. For $D = 15$ ft, $I = \frac{50}{15^2} = \frac{50}{225} = \frac{2}{9}$ foot-candle.

The Intensity I of Light Varies Inversely as the Square 1291 \frac { 2 } { 9 }192​

The Intensity I of Light Varies Inversely as the Square $1 \frac { 2 } { 9 }$