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A light source is located at P(1) as sh...

A light source is located at `P_(1)` as shown in the figure. All sides of the polygon are equal. The intensity of illumination at `P_(2)` is `I_(0)` . What will be the intensity of illumination at `P_(3)`

A

`(3 sqrt(3))/(8) I_(0)`

B

`(I_(o))/(8)`

C

`(3)/(8) I_(o)`

D

`(sqrt(3))/(8) I_(o)`

Text Solution

Verified by Experts

The correct Answer is:
A
`P_(1) P_(2) = 2a sin 60^(@)`
Now,
Intensity at `P_(2)`,
`I_(P_(2)) = (L)/((P_(1) P_(2))^(2)) `
= `(L)/((2a sin 60^(@))^(2) ) = (L)/(3a^(2))`
Intensity at `P_(3)` ,
`I_(P_(3)) = (L)/((P_(1) P_(3))^(2) + a^(2) ) cos 30^(@)`
= `(L)/((2a sin 60^(@))^(2) + a^(2) ) . (sqrt(3))/(2) = (sqrt(3L))/(8a^(2))`
`rArr I_(P_(3)) = (3 sqrt(3))/(8) I_(P_(2)) = (3sqrt(3))/(8) I_(0)`.
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