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

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

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 (1)/(D^2)`

Then,

`(I_1)/(I_2)=(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.

`(I_1)/(I_2)=(D_2^2)/(D_1^2)`

`\Rightarrow (2.7)/(I_2)=(70^2)/(56^2)`

`\Rightarrow (I_2)/(2.7)=(56^2)/(70^2)`

`\Rightarrow {I_2}=(56^2* 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.