# Light Intensity rate

• Jan 7th 2006, 12:03 PM
mathletes
Math Questttttttt
An object is moving away from the light source at a rate of 4 units/s. Find the rate of change of the intensity of illumination when it is 2 units from the light source.

yeah, this is my answer:
rate of change = k(1/unit˛xsecond)
:confused:
• Jan 7th 2006, 01:01 PM
CaptainBlack
Quote:

Originally Posted by mathletes
An object is moving away from the light source at a rate of 4 units/s. Find the rate of change of the intensity of illumination when it is 2 units from the light source.

yeah, this is my answer:
rate of change = k(1/unit˛xsecond)
:confused:

The intesity of illumination as a function of distance $\displaystyle r$ from a point source is:

$\displaystyle I(r)=I(1)/r^2$,

where $\displaystyle I(1)$ is the intensity of illumination at a distance of $\displaystyle 1$ unit from the source.

Now:

$\displaystyle \frac{d}{dt} I(r)=I(1)\frac{-2}{r^3}\ \frac{dr}{dt}$.

So now you only need to plug in $\displaystyle r=2$ and $\displaystyle \frac{dr}{dt}=4$ to get the answer, in units of
(whatever you are using as units of intensity)/s.

RonL
• Jan 7th 2006, 01:12 PM
mathletes
thank you, i obviously didn't know what i was doing.