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A point source is suspended at a hight h...

A point source is suspended at a hight `h = 1.0 m` over the centre of a round table of radius `R = 1.0 m`. The luminous intensity `I` of the source depends on direction so that illuminance at all points of the table is the same. Find the function `I (theta)`, where `theta` is the angle between the radiation direction and the vertical, as well as the luminous flux reaching the table if `I (0) = I_(0) = 100 cd`.

Text Solution

Verified by Experts

The illuminance at `P` is
`E_(P) = (I(theta))/((x^(2) + h^(2))) cos theta = (I(theta)cos^(3)theta)/(h^(2))`
since this is constant at all `x`, we must have
`I(theta) cos^(3) = const = I_(0)`
or `I (theta) = I_(0)//cos^(3) theta`
The luminous flux reaching teh table is
`Phi = piR^(2) xx (I_(0))/(h^(2)) = 314` lumen
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