Question

The intensity of light due to a point light source is inversely proportional to the square of the distance from the source.
If the intensity of light due to a point light source is $16Watts/m^2$ at a distance of 3.0 m from the source, what is the intensity at a distance of 12.0 m from the source?

• A. $8.0Watts/m^2$
• B. $4.0Watts/m^2$
• C. $2.0Watts/m^2$
• D. $1.0Watts/m^2$
• E. $32Watts/m^2$

Answer 1

The correct option is D $1.0Watts/m^2$

Given : $r_1=3.0$ m, $I_1=16$ Watts, $r_2=12.0$ m

Intensity of the light at a point, $I\propto \frac{1}{r^2}$ $⟹\frac{I_2}{I_1}=\frac{r_1^2}{r_2^2}$

$\therefore$ $\frac{I_2}{16}=\frac{(3.0{)}^2}{(12.0{)}^2}$ $⟹I_2=1.0$ $Watt/m^2$