Polarization Of Light

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Unpolarized light of intensity I0 passes first through an ideal polarizer and then a second polarizer whose axis is tilted at 60 degrees to the first.

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Polarization, as covered in NCERT, is analysed in two stages. When unpolarized light of intensity $I_0$ passes through the first ideal polarizer, exactly half is transmitted, giving $\frac{I_0}{2}$, because averaging over all orientations halves the intensity. The transmitted light is now polarized, so the second polarizer obeys Malus's law, $I=I_1\cos^2	heta$, with $	heta=60^\circ$. Since $\cos60^\circ=0.5$, we get $\cos^2 60^\circ=0.25$, so $I=\frac{I_0}{2}	imes0.25=\frac{I_0}{8}$. The value $\frac{I_0}{4}$ is wrong because it applies $\cos60^\circ$ once without squaring it. The value $\frac{I_0}{2}$ is wrong because it forgets the second polarizer entirely. The value $\frac{3I_0}{8}$ is wrong because it uses $\sin^2 60^\circ=0.75$ instead of $\cos^2 60^\circ$, applying the law to the wrong angle. As stated in NCERT Class 12, Chapter 10, an ideal polarizer halves unpolarized light, and Malus's law then governs a second polarizer. A magnitude check confirms the final intensity is less than the intermediate $\frac{I_0}{2}$, consistent with a tilted analyser cutting the beam further.

Polarization Of Light

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