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 $(E_{1})$ is:
$E_{1} = \frac{20}{{(0.4)}^{2}}$ .....(1)
∴ Illuminance due to the 80 cd source $(E_{2})$ is:
$E_{2} = \frac{80}{d^{2}}$ .....(2)
As, E₁ = E₂
$∴$ $\frac{20}{{(0.4)}^{2}}$ = $\frac{80}{d^{2}}$
⇒ d = 0.8 m = 80 cm.

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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?

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 sourceE1 is: E1=200.42 .....(1) ∴ Illuminance due to the 80 cd sourceE2 is: E2=80d2 .....(2) As, E1 = E2 ∴ 200.42 = 80d2 ⇒ d = 0.8 m = 80 cm.