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, f…

Question

asked Oct 6, 2021 118k views

1 Answer

Fidel Castro · Answer 1 · 2021-10-13T05:29:43+0000

Answer:

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

Explanation:

Given that,

The magnitude of intensity
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.