An electric lamp and a candle produce equal illuminance at a photometer screen when they are placed at 80 cm and 20 cm from the screen respectively. The lamp is now covered with a thin paper which transmits 49% of the luminous flux. By what distance should the lamp be moved to balance the intensities at the screen again?

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Solution

Let I₁ be the intensity when placed at a distance 80 cm and I₂ be the intensity when placed at a distance 20 cm apart from the screen.

Now,

$\frac{I_{1}}{I_{2}} = {(\frac{80}{20})}^{2} = 16$

According to the question, let the new distance between the lamp and the screen be x such that even after covering the lamp with a thin paper the intensities at the screen is balanced.

So,

$\frac{0.49 I_{1}}{I_{2}} = {(\frac{x}{20})}^{2} \Rightarrow 0.49 \times 16 \times 400 = x^{2} \Rightarrow x = 56 cm$

Thus, the lamp has to be moved by 80 cm - 56 cm = 24 cm.

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