Two polarizing filters are crossed (transmission axes at 90°) so that no light passes through. A third polarizer is inserted between them with its transmission axis at 45°. What happens?
ANo change — crossed polarizers block all light regardless of anything placed between them
BEven less light passes, since the third filter adds another layer of blocking
CSome light passes through, because the middle filter reorients the polarization state before it reaches the final filter
DAll light passes through, because the 45° filter cancels the effect of the crossed filters
The middle polarizer does not merely block — it transmits and reorients the polarization state. The first polarizer produces vertically polarized light. The 45° middle filter passes the cos²(45°) = 50% component along its axis; the exiting light is now polarized at 45°. The final filter (at 90° to the first but 45° to the middle) passes cos²(45°) = 50% of that light — roughly 25% passes the system when none did before. Option A is the classic misconception: polarizers are not simple blockers, they create new polarization states.
Question 2 Multiple Choice
A researcher claims to have produced 'polarized sound waves' by vibrating a speaker in one controlled direction. This claim is:
ACorrect — any wave can have its oscillation direction restricted
BCorrect only if the sound travels through a specially aligned medium
CIncorrect — sound is a longitudinal wave, and polarization requires transverse oscillations
DIncorrect — polarization requires an electromagnetic field, ruling out mechanical waves
Polarization means restricting oscillations to a specific direction within the plane perpendicular to propagation. This only makes sense for transverse waves, where oscillations are perpendicular to travel and can be oriented different ways. Sound is longitudinal — air molecules oscillate parallel to the direction of wave travel (compressions and rarefactions). There is no transverse direction to restrict, so polarization is physically meaningless for sound. Option D is also false: water waves are transverse mechanical waves and can be described with polarization.
Question 3 True / False
Polarization can only occur in transverse waves, not in longitudinal waves.
TTrue
FFalse
Answer: True
Polarization means restricting oscillations to a specific direction within the plane perpendicular to propagation. Only transverse waves have oscillations perpendicular to travel — and therefore a choice of orientation to restrict. Longitudinal waves (like sound) oscillate parallel to propagation, with no transverse direction available, so polarization is undefined for them.
Question 4 True / False
Inserting a third polarizing filter between two crossed polarizers can primarily reduce the transmitted intensity, seldom increase it.
TTrue
FFalse
Answer: False
This is wrong, and the three-polarizer experiment demonstrates it dramatically. Two crossed polarizers transmit zero light. Inserting a third at 45° between them transmits approximately 25% of the light entering the system. The middle polarizer reorients the polarization state — light exiting it is polarized at 45°, which is no longer perpendicular to the final filter's axis. The third filter increases transmitted intensity from zero to a positive value. Polarizers are not merely absorbers; they actively create new polarization states.
Question 5 Short Answer
Why does inserting a polarizer at 45° between two crossed polarizers allow light to pass through the system, even though the crossed polarizers alone transmit nothing?
Think about your answer, then reveal below.
Model answer: The first polarizer produces vertically polarized light. Two crossed polarizers block all light because the second filter's horizontal axis is perpendicular to vertical polarization — zero component survives. The middle filter at 45° projects the vertical polarization onto its 45° axis (transmitting cos²45° = 50% intensity), producing light now polarized at 45°. This 45°-polarized light then hits the final horizontal filter: 45° is not perpendicular to horizontal, so a nonzero component (cos²45° = 50%) passes. The key is that the middle polarizer does not just attenuate — it creates a new polarization state that can couple to the final filter.
The math: first filter → I₀ vertically polarized. Middle filter → I₀/2 at 45°. Final filter → I₀/4 (horizontal). Each step involves a genuine reorientation of the polarization state, not just absorption. This is why the sequence 'vertical → 45° → horizontal' transmits light while 'vertical → horizontal' transmits none.