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 Intensityof light after transmission from first polaroid  =I02Intensity of light emitted from P3I1=I02cos2⁡θIntensity of light transmitted from polaroid i.e., fromP2=I1cos2⁡90∘−θ=I02cos2⁡θsin2⁡θP2=I08(2sin⁡θcos⁡θ)2=I08sin2⁡2θ