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An illuminant shaped as a plane horizont...

An illuminant shaped as a plane horizontal disc `S = 100 cm^(2)` in area is suspended over the centre of a round table of radius `R = 1.0 m`. Its luminance does not depend on direction and is equal illuminant be suspended to provide maximum illuminance at the circumference of the table ? How great will that illuminance be? The liuminant is assumed to be a point source.

Text Solution

Verified by Experts

The equivalent luminous intensity in the direction `OP` is
`L S cos theta`
and the illuminance at `P` is
`(L S cos theta)/((R^(2) + h^(2))) cos theta = (LSh^(2))/((R^(2) +h^(2))^(2))``=(LS)/(((R^(2))/(h) + h)^(2)) = (LS)/([((R)/(sqrt(h)) - sqrt(h))^(2)+2R]^(2))`

This is maximum when `R = h`
and the maximum illuminance is
`(LS)/(4R^(2)) = (1.6 xx 10^(2))/(4) = 40` lux
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