Polarized Light Transmission Through a Filter

Steps:

• The incident wave's electric field vector has magnitude A and lies in its plane of polarization.
• The filter transmits only the component of the electric field parallel to its transmission axis.
• The parallel component is A cosθ, where θ is the angle between the incident polarization plane and the transmission axis.
• Thus, the emerging wave has amplitude A cosθ.

Why C is correct:

• By the projection of the electric field vector, the transmitted amplitude is A cosθ, per the definition of vector components for polarized waves.

Why the others are wrong:

• A omits the factor of A, giving only the angular dependence, not the full amplitude.
• B and D give A cos²θ, which is the form for transmitted intensity (proportional to amplitude squared), not amplitude.

Final answer: C