Malus's Law: Transmitted Amplitude Ratio

Steps:

• Vertically polarized light has electric field at 90° to horizontal.
• Filter's transmission axis is at 40° to horizontal.
• Angle θ between polarization and axis is 90° - 40° = 50°.
• Transmitted amplitude ratio = cosθ = cos50° ≈ 0.64.

Why C is correct:

• Malus's law states transmitted amplitude = incident amplitude × cosθ, where θ is the angle between incident polarization and transmission axis; cos50° = 0.6428 ≈ 0.64.

Why the others are wrong:

• A: 0.41 ≈ cos66° or sin24°, wrong angle.
• B: 0.59 ≈ cos54°, incorrect θ.
• D: 0.77 ≈ cos40° or sin50°, uses filter angle directly.

Final answer: C