NEET-XII-Physics
22: Photometry
- #15An 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?Ans : 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}}={\left(\frac{80}{20}\right)}^{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}}={\left(\frac{x}{20}\right)}^{2}``
`` \Rightarrow 0.49\times 16\times 400={x}^{2}``
`` \Rightarrow x=56\,\mathrm{\,cm\,}``
Thus, the lamp has to be moved by 80 cm - 56 cm = 24 cm.
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