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A circular area of radius 1.0 cm is plac...

A circular area of radius 1.0 cm is placed at a distance of 2.0 m from a poit source.Teh source emits light uniformluy in al directions. The line joining the sorce to the dcentre of the area is normal to the area. It ils found that `2.0xx1^-3` lumen of luminous flux is incident on the area. Calculate the total luminous flux emitted by the soure and teh luminous intensity of the source along the axis of the area.

Text Solution

Verified by Experts

Thesoid angle subtended by the area on the point source is
`/_\omega=(pi(1.0cm)^2)/((2.0m)^2)=pi/4xx10^-4sr`.
Thus `2.0xx10^-3` lumen of flux is emitted in `pi/4xx10^-4` sr. The total solid angle at the source is 4pi. As the source radiates uniformly in all directions, the total luminous flux is
`F=(4pi)/(pi/4xx10^-4)xx2.0xx10^-3lumen`
`=320 lumen.
the luminous intensity =/_\F//_\omega`
`=(2.0xx10^-3lumen)/(pi/4xx10^-4sr)=25cd`
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