Q.When unpolarized light is passed through a polarizer, its intensity (A) increases
(B) decreases
(C) remains unchanged
(D) depends on the orientation of the polarizer

[!TLDR] A single polarizer always halves the intensity of unpolarized light, REGARDLESS of its orientation, since the incident field's random direction has …

As derived in Section 7.7, unpolarized incident light has its electric field spread with equal likelihood over every angle $\phi$ from 0° to 180° relative to any chosen axis. The intensity transmitted by a polarizer for a given incoming field direction is proportional to $\cos^2\phi$, and averaging this over all equally-likely values of $\phi$ gives exactly 1/2, REGARDLESS of what angle the polarizer's own axis happens to be set at (rotating the polarizer just relabels which incoming directions count as $\phi=0$; the average over all directions is unchanged). So the intensity ALWAYS decreases, specifically to exactly half its original value, for ANY orientation of a single polarizer acting on unpolarized light. Option (D) -- 'depends on orientation' -- would be the correct description …

Distinguish the two different rules: unpolarized light through the FIRST polarizer always loses exactly half its intensity regardless of orientation (averaging over all random incoming field directions); only a SECOND polarizer, actin …

Applying Malus' Law's 'depends on the angle' logic to a FIRST polarizer acting on unpolarized light, when that angle-dependence only applies to a second polar …