Polarized light through two filters at 45° using Malus's law

Steps:

• Assume incident polarization aligns with first filter's axis, so without second filter, intensity is I₀.
• Light hits inserted second filter at 45° to incident polarization: transmitted intensity I₁ = I₀ cos²45° = I₀ (½) = I₀/2, now polarized along second filter's axis.
• This light then hits first filter at 45° relative angle: final intensity I = I₁ cos²45° = (I₀/2) (½) = I₀/4.

Why C is correct:

• Malus's law states transmitted intensity = incident intensity × cos²θ, where θ is angle between polarization direction and transmission axis; applied sequentially for two filters.

Why the others are wrong:

• A: Intensity 0 occurs only for 90° crossed polarizers, not 45°.
• B: I₀/8 results from larger angles or additional filters, not this setup.
• D: I₀/2 is intensity after single 45° filter, ignoring the second.

Final answer: C