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प्रश्न
Two polaroids ‘A’ and ‘B’ are kept in crossed position. How should a third polaroid ‘C’ be placed between them so that the intensity of polarized light transmitted by polaroid B reduces to 1/8th of the intensity of unpolarized light incident on A?
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उत्तर
Let θAC, angle between the transmission axis of Polaroid A and Polaroid C.
θCB, angle between the transmission axis of Polaroid C and Polaroid B.
Then,
θAC + θCB = 180° (As, Polaroid ‘A’ and ‘B’ are kept in crossed position.)
Or, θAC = 180° − θCB ... (1)
Intensity of unpolarized light = I0
I1, I2 and I3 are the intensities of light on passing through the A, B and C polarises respectively.
Now,
`I_1 = 1/2I_0 .....(2)`
`I_2 =I_1cos^2theta_(AC)`
=`1/2I_0cos^2theta_(AC)`
`= 1/2I_0 cos^2(180° -theta_(CB))` (from equation (1))
`I_2=1/2I_0sin^2theta_(CB)......... (3)`
and, `I_3 =I_2cos^2theta_(CB)`
`I_3=(1/2I_0sin^2theta_(CB)) cos^2theta_(CB)`
or,`I_3 = 1/2I_0sin_2theta_(CB)cos^2theta_(CB)`
As,given, `I_3=1/8 I_0`
Therefore,`1/8I_0 =1/2I_0 xx 1/4(sin2theta_(CB))^2`
`or, sin 2 theta_(CB =1)`
`or, 2theta_(CB) =90°`
`or, theta_(CB) =45°`
Thus, Polaroid ‘C’ must be placed at angle 45° with Polaroid ‘B’.
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