Two polaroids are placed in the path of unpolarized beam of intensity I0 such that no light is emitted from the second polaroid. If a third polaroid whose polarization axis makes an angle θ with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be

No light is emitted from the second polaroid, so P1 and P2 are perpendicular to each other Let the initial intensity of light is I0. So intensity of light after transmission from first polaroid =I02 .   Intensity of light emitted from  P3=I1=I02cos2θ  Intensity of light transmitted from last polaroid i.e. from P2=I1cos2(900−θ)=I02cos2θ.sin2θ=I02×4(4sin2θcos2θ) =I08(2sinθcosθ)2=I08sin22θ∵θ1+θ2=90 ,sin2θ=2sinθcosθ