When unpolarized light passes through a single polaroid filter, approximately what fraction is transmitted?

When unpolarized light passes through a single polaroid filter, approximately what fraction is transmitted?

• A. All
• B. One quarter
• C. Roughly half
• D. None

Answer: (C)

Unpolarized light contains waves vibrating in all polarization directions, so a polarizer can only pass the portion that aligns with its transmission axis. Since the polarization directions are uniformly distributed, the average transmitted component is the projection of the electric field along that axis, which, when averaged over all angles, comes out to about half of the incident intensity. In other words, once the light hits a single polarizer, roughly half of it gets through. If the light were already polarized, Malus’s law would apply and the transmitted intensity would depend on the angle between the light’s polarization and the polarizer’s axis, following I_out = I_in cos^2(theta). But for unpolarized light, that angle is effectively random, so the average outcome is half.

Unpolarized light contains waves vibrating in all polarization directions, so a polarizer can only pass the portion that aligns with its transmission axis. Since the polarization directions are uniformly distributed, the average transmitted component is the projection of the electric field along that axis, which, when averaged over all angles, comes out to about half of the incident intensity. In other words, once the light hits a single polarizer, roughly half of it gets through.

If the light were already polarized, Malus’s law would apply and the transmitted intensity would depend on the angle between the light’s polarization and the polarizer’s axis, following I_out = I_in cos^2(theta). But for unpolarized light, that angle is effectively random, so the average outcome is half.