Question

Two light sources of intensities 8 cd and 12 cd are placed on the same side of a photometer screen at a distance of 40 cm from it. Where should a 80 cd source be placed to balance the illuminance?

Answer 1

Total intensity of the 8 cd and the 12 cd light source is 20 cd.

Let d be the distance of the 80 cd source.

∴ Illuminance due to the 20 cd source (E₁) is

\[E_1  = \frac{20}{\left( 0 . 4 \right)^2}..........(1)\]

∴ Illuminance due to the 80 cd source (E₂) is

\[E_2  = \frac{80}{d^2}............(2)\]

As, E₁ = E₂

\[\therefore\frac{20}{\left( 0 . 4 \right)^2}=\frac{80}{d^2}\]

⇒ d = 0.8 m = 80 cm.