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The overall luminous efficient of a 100 ...

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.

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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.
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