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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 polaroid. If a third polaroid whose polarization axis makes an angle \( \theta \) with the polarization axis of first polaroid, is placed between these polaroids, then the intensity of light emerging from the last polaroid will be
(a) \( \left(\frac{I_{0}}{8}\right) \sin ^{2} 2 \theta \)
(b) \( \left(\frac{I_{0}}{4}\right) \sin ^{2} 2 \theta \)
(c) \( \left(\frac{I_{0}}{2}\right) \cos ^{4} \theta \)
(d) \( I_{0} \sin ^{4} \theta \)
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