The illuminance of a small area changes from 900 lumen to 400 lumen when it is shifted along its normal by 10 cm. Assuming that it is illuminated by a point source placed on the normal, find the distance between the source and the area in the original position.

Question

The illuminance of a small area changes from 900 lumen to 400 lumen when it is shifted along its normal by 10 cm. Assuming that it is illuminated by a point source placed on the normal, find the distance between the source and the area in the original position.

Philoid · Accepted Answer

Let the luminous intensity of the source be and the distance between the source and the area, in the initial position, be .
Given,
Initial illuminance (E_A) = 900 lumen
Final illuminance (E_B) = 400 lumen

Illuminance on the initial position is given by:

----------- (i)

Illuminance at final position is given by:

----------- (ii)

Equating luminous intensity from (i) and (ii), we get:

⇒

The distance between the source and the area at the initial phase was 20 cm.