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A point source emitting uniformly in all...

A point source emitting uniformly in all directions is placed above a table top at a distance of 0.50 m from it. The luminous flux of the source is 1570 lumen. Find the illuminance at a small surface area of the table to a.directly below the source and b. at as distance of 0.80 m from the source.

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Consider the situation shown in ure. Let A be the point directly below the source S and B be the point at 0.80 m from the source.

The luminous flux o f1570 lumen is emitted uniformly in the solid angle `4pi`. The luminous intensity of the source in any direction is
`I=(1570 lumen)/(4pisr)`
=125cd.
The illumiN/Ance is
`E=(Icostheta)/r^2`
`At the point A, r=0.50 m and theta= 0.` thus.
`E_A=(125cd)/(0.255m^2)=500`lux`
At the point B, r=0.80 =/m and `costheta=(SA)/(SB)=0.50/0.80=5/8`
thus, `E_B=((125cd)xx5/8)/(0.64m^2)`
`==122lux.
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