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 [tex]I[/tex] of light varies inversely as the square of the magnitude of distance D from the source.
That is
[tex]I\propto \frac{1}{D^2}[/tex]
Then,
[tex]\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}[/tex]
Given that,
The magnitude of intensity of illumination on a screen 56 ft from a light is 2.7 foot-candle.
Here,
[tex]I_1[/tex]=2.7 foot-candle, [tex]D_1[/tex]= 56 ft
[tex]I_2[/tex]=?, [tex]D_2[/tex]= 70 ft.
[tex]\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}[/tex]
[tex]\Rightarrow \frac{2.7}{I_2}=\frac{70^2}{56^2}[/tex]
[tex]\Rightarrow \frac{I_2}{2.7}=\frac{56^2}{70^2}[/tex]
[tex]\Rightarrow {I_2}=\frac{56^2\times 2.7}{70^2}[/tex]
[tex]\Rightarrow {I_2}=1.728[/tex] foot-candle
The intensity on a screen 70 ft from the light is 1.728 foot candle.
