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 20 ft from the light.
A) $1 \frac { 1 } { 8 }$ foot-candles
B) $\frac { 1 } { 8 }$ foot-candle
C) $\frac { 1 } { 9 }$ 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 20 ft from the light. 
A) $1 \frac { 1 } { 8 }$ foot-candles
B) $\frac { 1 } { 8 }$ foot-candle
C) $\frac { 1 } { 9 }$ foot-candle
D) 2 foot-candles

Quizplus · Accepted Answer

The intensity of light varies inversely as the square of the distance, so $I_1D_1^2 = I_2D_2^2$. Given $I_1 = 2$ foot-candles at $D_1 = 5$ ft, and $D_2 = 20$ ft, we find $I_2$ by substituting: $2 \times 5^2 = I_2 \times 20^2$, which simplifies to $I_2 = \frac{1}{8}$ foot-candle.

The Intensity I of Light Varies Inversely as the Square 1181 \frac { 1 } { 8 }181​

The Intensity I of Light Varies Inversely as the Square $1 \frac { 1 } { 8 }$