The intensity I of light bulb varies inversely as the square of the distance d from the light bulb. Suppose I is 250 w/m^2 when the distance is 5 m. How much farther would it be to a point where the intensity is 40 w/m^2?

Question

The intensity I of light bulb varies inversely as the square of the distance d from the light bulb.  Suppose I is 250 w/m^2 when the distance is 5 m.  How much farther would it be to a point where the intensity is 40 w/m^2?

anonymous · Answer

since they vary inversely..
I * d = constant
so in first case   I1*d1 = 250*5 = 1250

so I2 * d2 should also be 1250 in second case
40 * d2 = 1250
d2 = 1250/40 = 31.25


d1 = 5
d2 = 31.25

So it would be 31.25 - 5 = 26.25 m further to the point where the intensity is 40 w/m^2