A light wave has E-field oscillating at right angle to its direction of propagation. A polarizer allows only the component of E-field in the polarizer’s orientation to pass through.

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So the first polarizer polarizes the unpolarized light. Because an unpolarized light has light in all orientations, its intensity always drops to half after passing through the first polarizer, regardless of how the polarizer is oriented.

If the second polarizer is oriented at the same angle as the first, then 100% of the polarized light is passed through. If the second polarizer is perpendicular to the first, then 0% of the polarized light is passed through. If the second polarizer is misaligned with the first by an angle θ, the amplitude of the polarized light will drop from E₀ to E₀cosθ, and the intensity will drop from I₀ to I₀cos₂θ.

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