Two polaroids are placed in the path of unpolarized beam of intensity I_(0) such that no light is emitted from the second polarid. If a third polaro

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Two polaroids are placed in the path of unpolarized beam of intensity I_(0) such that no light is emitted from the second polarid. If a third polaroid whose polarization axis makes an angle theta with the polarization axis of first polaroid, is placed between these two polariods then the intensity of light emerging from the last polaroid will be
A. (a) (I_0/8)sin^2 2theta
B. (b) (I_0/4)sin^2 2theta
C. (c) (I_0/2)cos^4theta
D. (d) I_0cos^4theta

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No light is emitted from the second polaroid, so P_1 and P_2 are perpendicular to each other

Let the initial intensity of light is I_0. So intensity of light after transmission from first polaroid=I_0/2.
Intensity of light emitted from P_3, I_1=I_0/2cos^2theta
Intensity of light transmitted from last polaroid, i.e., from P_2=I_1cos^2(90^@-theta)=I_0/2 cos^2theta.sin^2theta
=I_0/8(2sinthetacostheta)^2=I_0/8sin^2 2theta