Question

The brightness of the illumination of an object varies inversely as the square of the distance from the object to the source of light. How far from a bulb does an object recieve four times as much illumination as it does when it is 8 m from the bulb?

Answer 1

"The brightness of the illumination of an object varies inversely as the square of the distance from the object to the source of light."
OR
\[I=\frac{net power}{surface area}=\frac{P}{4\pi r^2}\]

Answer 2

Your looking for:
\[\frac{I_2}{I_1}=...\]

Answer 3

I don't know bout this -.- sorry

Answer 4

Are you OK with:
\[I=\frac{netpower}{surfacearea}=\frac{P}{4πr^2}\]

Answer 5

No , i don't know that

Answer 6

That is the formula for light intensity of a source with total power P at a distance of r.

Answer 7

The distance is the only given how can i answer it??

Answer 8

We don't need to know the power of the light source.
The question wants us to find out how far from the bulb (r=?) do we get four times as much light intensity than at 8m from the bulb.
\[I_2=4I_1\]
Agreed?

Answer 9

Yea

Answer 10

But hould i get that?

Answer 11

Wait... Let math do it's magic!
We know the formula for light intensity:
\[I_1=\frac{P}{4 \pi r_1^2}\]
\[I_2=\frac{P}{4 \pi r_2^2}\]
We are investigating one light source, so P is the same for both. However, we are investigating light intensity at two different locations, one at r_1 and another at r_2.
Agreed?

Answer 12

Okay, and then?

Answer 13

What do you get?