Polarization Of Light

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, $I=I_1{\cos }^2\theta$, with $\theta =60^{\circ }$. Since $\cos 60^{\circ }=0.5$, we get ${\cos }^{2}60^{\circ }=0.25$, so $I=\frac{I_0}{2}\times 0.25=\frac{I_0}{8}$. The value $\frac{I_0}{4}$ is wrong because it applies $\cos 60^{\circ }$ 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.