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A lamp (point source) is hanging along t...

A lamp (point source) is hanging along the axis of a circular table of radius r. At what height should the lamp be placed above the table so that the illuminance at the edge of the table is `(1)/(8)` of that at its centre?

A

A)`r/2`

B

B`(r)/(sqrt2)`

C

C)`(r)/(sqrt3)`

D

D)`(r)/(sqrt7)`

Text Solution

Verified by Experts

The correct Answer is:
C
`E _(1) = (I)/(h ^(2))" "...(1)`

and `E _(2) = ( I cos theta )/(( sqrt ( h ^(2) + r ^(2))) ^(2))" "...(2)`
`= ( I xx h )/( ( h ^(2) + r ^(2)) ^( 3//2))`
`therefore (E _(2))/(E_(1)) = (1)/(8) = (h ^(3))/( ( h ^(2) + r ^(2)) ^( 3//2))`
`implies ( h ^(2) + r ^(2))^( 1//2) = 2h implies h ^(2) = (r)/( sqrt3)`
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