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Two nicols are so oriented that the maxi...

Two nicols are so oriented that the maximum amount of light is transmitted. To what fraction of its maximum value is the intensity of transmitted light reduced when the analyser is rotated through (i) `30^(@)` (ii) `60^(@)` ?

Text Solution

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Net intensity transmitted is
`I = I_(0) cos^(2) theta`
(i) Here, `theta = 30^(@)`
`:. I = I_(0) (cos 30^(@))^(2) = I_(0) ((sqrt(3))/(2))^(2)`
`I = (3)/(4)I_(0) = 0.75 I_(0) = 75% I_(0)`
`:.` Intensity transmitted is reduced to `75%` of the maximum intensity.
(ii) Here, `theta = 60^(@)`
`I = I_(0) cos^(2) theta = I_(0) (cos 60^(@))^(2)`
`= (I_(0))/(4) = 0.25I_(0) = 25% I_(0)`
`:.` Intensity transmitted is reduced to `25%` of the maximum intensity.
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