Question

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

• A. $24cm$
• B. $12cm$
• C. $18cm$
• D. $456cm$

Answer 1

Answer: (A)

$24cm$

Case(i)
$\frac{I_1}{I_2}$ = ${\left(\frac{80}{20}\right)}^2$

Case(II)
$\frac{.49I_1}{I_2}$ =${\left(\frac{d}{20}\right)}^2$

$d$ = $20\sqrt{.49\left(16\right)}$ = $20\left(2.8\right)$
= $56$cm
Lamp be moved by $80$ - $56$ = $24$ cm