question_answer

An electric bulb illuminates a plane surface. The intensity of illumination on the surface at a point 2m away from the bulb is\[5\,\,\times \,\,{{10}^{-}}^{4}phot\text{ }\left( lumen/c{{m}^{2}}\text{ } \right)\]. The line joining the bulb to the point makes an angle of \[60{}^\circ \] with the normal to the surface. The intensity of the bulb in candela is

A) \[40\sqrt{3}\]                

B) 40

C) 20                                

D) \[40\times {{10}^{-4}}\]

Correct Answer: B

Solution :

\[I=\frac{L\,\cos \,\theta }{{{r}^{2}}}\] \[\Rightarrow \,\,\,\,\,L=\frac{I\times {{r}^{2}}}{\cos \,\theta }\] \[=\,\frac{5\times {{10}^{-4}}\times {{10}^{4}}\times {{2}^{2}}}{\cos \,60{}^\circ }\,\,=\,\,40\,\,Candels\]