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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?
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Solution
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.
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