Proportions and Variations

Question

The Intensity I of light from a light bulb varies inversley as the square of the distance d from the light bulb. Suppose I is 360 w/m (squared) when the distance is 3 m. How much farther would it be to a point where the Intensity is 250 w/m(squared)?

Answer 1

The Intensity I of light from a light bulb varies inversley as the square of the distance d from the light bulb.

Creating a formula from this information gives us,

I = k/d^2, where k is a constant of proportionality.

I is 360 w/m (squared) when the distance is 3 m. From this we can write,

360 = k/3^2

Therefore k = 360*9 = 3,240.

How much farther would it be to a point where the Intensity is 250 w/m(squared)?

When I = 250 w/m^2,

250 = 3,240/d^2

d^2 = 3,240/250 = 12.96

d = 3.6 m.

The second point is 3.6 - 3.0 = 0.6m from the 1st point