Lamp post distance problem

Question

A 10 cd point source lamp and a 50 cd point source lamp cast equal intensities on a wall. If the 10 cd lamp is 8.0 m from the wall, how far is the 50 cd lamp?

____m

Answer 1

All other things being equal, the illuminance (the amount of light falling on a surface) follows an inverse square law: double the distance and the illuminance goes down by 4.

Also, all other things being equal, the illuminance is proportional luminous flux.

So: L1/(D1^2) = L2/(D2^2) or

D2 = sqrt(D1^2 L2 / L1) = D1 sqrt (L2/L1)