question_answer

Two lamps of luminous intensity of 8 Cd and 32 Cd respectively are lying at a distance of 1.2 m from each other. Where should a screen be placed between two lamps such that its two faces are equally illuminated due to two sources

A)            10 cm from 8 Cd lamp       

B)            10 cm from 32Cd lamp

C)            40 cm from 8 Cd lamp       

D)            40 cm from 32 Cd lamp

Correct Answer: C

Solution :

                   \[I=\frac{L}{{{r}^{2}}}\Rightarrow \frac{{{L}_{1}}}{{{L}_{2}}}=\frac{r_{1}^{2}}{r_{2}^{2}}\]            or \[\frac{8}{{{x}^{2}}}=\frac{32}{{{(120-x)}^{2}}}\]            Solving it we get\[x=40\,cm\].