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 56 ft from a light is 2.7 foot-candles, find the intensity on a screen 70 ft from the light.

Answer 1

Answer:

The intensity on a screen 70 ft from the light is 1.728 foot candle.

Step-by-step explanation:

Given that,

The magnitude of  intensity $I$ of light varies inversely as the square of the magnitude of distance D from the source.

That is

$I\propto \frac{1}{D^2}$

Then,

$\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}$

Given that,

The magnitude of intensity of illumination on a screen 56 ft from a light is 2.7 foot-candle.

Here,

$I_1$=2.7 foot-candle, $D_1$= 56 ft

$I_2$=?, $D_2$= 70 ft.

$\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}$

$\Rightarrow \frac{2.7}{I_2}=\frac{70^2}{56^2}$

$\Rightarrow \frac{I_2}{2.7}=\frac{56^2}{70^2}$

$\Rightarrow {I_2}=\frac{56^2\times 2.7}{70^2}$

$\Rightarrow {I_2}=1.728$ foot-candle

The intensity on a screen 70 ft from the light is 1.728 foot candle.