# Inversely proportional

Printable View

• November 1st 2008, 02:08 AM
helloying
Inversely proportional
A spot in the room is illuminated by a lamp, dcm away.The intensity I of the light spot is inversely proportional to the square of d. At certain distance d cm, the intensity is 60 units. What is the intensity when the distance is doubled?
• November 1st 2008, 02:19 AM
mr fantastic
Quote:

Originally Posted by helloying
A spot in the room is illuminated by a lamp, dcm away.The intensity I of the light spot is inversely proportional to the square of d. At certain distance d cm, the intensity is 60 units. What is the intensity when the distance is doubled?

$I = \frac{k}{d^2}$.

$60 = \frac{k}{d_1^2}$ .... (1)

$I_2 = \frac{k}{(2d_1)^2} = \frac{k}{4 d_1^2} = \frac{1}{4} \, \frac{k}{d_1^2}$ .... (2)

Substitute (1) into (2).