As shown in figures, three identical polaroids \(P_1\), \(P _2\) and \(P _3\) are placed one after another. The pass axis of \(P_2\) and \(P_3\) are inclined at angle of \(60^{\circ}\) and \(90^{\circ}\) with respect to axis of \(P _1\). The source \(S\) has an intensity of \(256 \frac{ W }{ m ^2}\). The intensity of light at point \(O\) is \(...........\frac{ W }{ m ^2}\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.