Question

The overall luminous efficient of a 100 W electric lamp is 25 lumen `W^-1`. Assume that light is emitted by the lamp only in the forward half, and is uniformly distributed in al diredctionsin this half. Calculate the luminous flux falling on a plane object of area `1cm^2` placed at a distance of 50 cm from the lamp and perpendicular to the line joining the lamp and the object.

Answer 1

The power input to te bulb =100 W
The luminous flux emitted by the bulb
`=(25 lumen W^-1)xx100W` ltbrge2500lumen`
Since light is emitted only in the forward half and is distributed uniformly in this halt the luminous intensityis
`I/_F//_omega`
`=(2500lumen)/(2pisr)`
the solid angle subtended by the object on the lamp is
`=/_omega=(1cm^2)/((50 cm)^2)=1/2500sr`.
the luminous flux emitted in this solid angle is
`/_F=I/_omega`
`=(2500/(2pi) lumen/sr)(1/2500sr)`
`1/(2pi) lumen =0.16 lumen.