Malus's law (1809): $I = I_0\cos^2\theta$ where $I_0$ = intensity of incident plane-polarized light; $\theta$ = angle between polarization direction and analyzer transmission axis.

Step-by-step analysis of multi-polaroid systems:

Two polaroids (analyzer at $\theta$):

• After P1 (if unpolarized): $I_1 = I_0/2$
• After P2 (Malus): $I_2 = (I_0/2)\cos^2\theta$

Three polaroids (P1, P2 at $\alpha$, P3 at 90° to P1):

• $I_1 = I_0/2$
• $I_2 = (I_0/2)\cos^2\alpha$
• $I_3 = (I_0/2)\cos^2\alpha\cdot\cos^2(90°-\alpha) = (I_0/2)\cos^2\alpha\sin^2\alpha = (I_0/8)\sin^2(2\alpha)$
• Maximum at $\alpha = 45°$: $I_3 = I_0/8$

Common results for NEET: