Question

The intensity of light due to a point light sources is inversely proportional to the square of the distance from the source.
If the intensity of light due to a point light source is $16/Watts/m^2$ at a distance of $3.0m$ from the source, what is the intensity at a distance of $12.0m$ 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 $1.0Watts/m^2$

Intensity at a point $r$ distance away, $I=\frac{I_o}{r^2}$

$⟹$ $\frac{I_2}{I_1}=\frac{r_1^2}{r_2^2}$

Given : $I_1=16.0$ $Watts/m^2$, $r_1=3.0$ m, $r=12.0$ m

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