Questions: Polarization of Electromagnetic Waves

Question 1

Two ideal linear polarizers are oriented with their transmission axes crossed at 90°, blocking nearly all light. A third polarizer is inserted between them at 45° to each. What happens?

• A. No light passes — two crossed polarizers block all light regardless of what is inserted between them
• B. Some light passes — the middle polarizer projects the first polarizer's output onto its own axis and rotates the polarization, allowing the final polarizer to transmit a fraction
• C. All the original intensity is restored, since the middle polarizer cancels the effect of the outer two
• D. Light is blocked more effectively because three filters are more absorbing than two

Answer: (B)

After the first polarizer, light is linearly polarized. The middle polarizer at 45° transmits cos²(45°) = ½ of that intensity and rotates the polarization to 45°. The final polarizer is now only 45° from the incoming polarization and transmits another cos²(45°) = ½, giving total transmission of ¼ of I₀/2 = I₀/8. Option (a) is the key misconception — crossed polarizers block light only when light arrives already polarized along one axis. Inserting a polarizer at 45° breaks this by rotating the polarization state at each step.

Question 2

What two conditions are required to produce circularly polarized light by superimposing two orthogonally polarized waves?

• A. Equal amplitudes and a frequency difference of exactly ω/2
• B. Equal amplitudes and a phase difference of exactly 90°
• C. Unequal amplitudes and a phase difference of 90°
• D. Equal amplitudes traveling in opposite directions along the propagation axis

Answer: (B)

Circular polarization requires (1) equal amplitudes in the two orthogonal components and (2) a 90° phase difference. If the amplitudes are unequal, the tip of E⃗ traces an ellipse, not a circle. If the phase difference is not 90°, the result is also elliptical. Elliptical polarization is the general case; circular and linear are special limits. Option (d) confuses polarization with standing waves.

Question 3

Elliptical polarization is the most general polarization state — both linear and circular polarization are special limiting cases of elliptical polarization.

• T. True
• F. False

Answer: True

Any polarization state can be described as the superposition of two orthogonal linearly polarized components with some amplitude ratio and phase difference. When the amplitudes are equal and the phase difference is 90°, the ellipse becomes a circle (circular polarization). When the phase difference is 0° or 180°, the ellipse collapses to a line (linear polarization). All other combinations produce an ellipse, making elliptical polarization the general form.

Question 4

Unpolarized light, such as sunlight, has its electric field oscillating in most directions, including along the direction of propagation.

• T. True
• F. False

Answer: False

Electromagnetic waves are transverse — the electric field E⃗ is always confined to the plane perpendicular to the direction of propagation. Unpolarized light does not oscillate along the propagation direction; rather, its polarization direction varies randomly and rapidly within the transverse plane. A longitudinal electric field component would violate Maxwell's equations for EM waves in vacuum.

Question 5

Why can electromagnetic waves be polarized but sound waves cannot?

Model answer: Sound waves are longitudinal — particle displacement is parallel to the direction of propagation. There is only one direction of displacement, so there is no transverse degree of freedom to describe. Electromagnetic waves are transverse — the electric field vector lies in the plane perpendicular to propagation. Within that plane, E⃗ can point in any direction or rotate, giving rise to different polarization states. Polarization is a property of transverse waves only.

This distinction has practical consequences: polarizers work by selecting one orientation of the electric field. No equivalent device exists for sound because sound has no transverse degree of freedom to select. Understanding why polarization exists requires recognizing that 'transverse' means there are two independent directions in the plane perpendicular to propagation, and polarization describes how the wave distributes energy between them.