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Two beams, A and B, of plane polarized l...

Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of polaroid through `30^(@)` makes the two beams appear equally bright. If the initial intensities of the two beams are `I_(A) and I_(B)` respectively, then `I_(A)// I_(B)` equals:

A

`(1)/(3)`

B

3

C

`(3)/(2)`

D

1

Text Solution

Verified by Experts

According to Malus' law, `I = I_(0)cos^(2) theta`
`therefore " " I_(A') = I_(A) cos^(2) theta_(1)`
`= I_(A)cos^(2) 30^(@) = (3)/(4) I_(A) " " [therefore theta_(1) = 30^(@)]`
Again, `I_(B') = I_(B)cos^(2) theta_(2) `
`= I_(B)cos^(2) 60^(@) = (1)/(4)I_(B) [because theta_(2) = 90^(@) - theta_(1) = 60^(@)]`
According to question, `I_(A') = I_(B')`
or, `(3)/(4)I_(A) = (1)/(4)I_(B) " " or, (I_(A))/(I_(B)) = (1)/(3)`
The option (A) is correct.
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