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?

#### Solution

Let I_{1} be the intensity when placed at a distance 80 cm and I_{2} be the intensity when placed at a distance 20 cm apart from the screen.

Now,

\[\frac{I_1}{I_2} = \left( \frac{80}{20} \right)^2 = 16\]

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

So,

\[\frac{0 . 49 I_1}{I_2} = \left( \frac{x}{20} \right)^2 \]

\[ \Rightarrow 0 . 49 \times 16 \times 400 = x^2 \]

\[ \Rightarrow x = 56 cm\]

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