======Three Polarizing Filters======


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**Alternative titles:** Crossed Polarizers with 45° Insert
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====Summary====                   
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====Procedure====  
  - Gather two identical linear polarizing sheets (A and B), a third sheet (C), a bright, diffuse light source or projector, and a sheet of white paper as a screen.
  - Hold A in front of the light and observe that transmitted light is dimmer (unpolarized → linearly polarized).
  - Place B directly behind A with its axis parallel to A. Rotate B to find maximum transmission when axes are aligned.
  - Rotate B to 90° relative to A (crossed). Show that transmission drops nearly to zero.
  - Insert C between A and B with its transmission axis at ~45° to both. Observe that light now passes through the stack A–C–B, despite A and B being crossed.
  - Swap the order (e.g., B–C–A) and repeat. Emphasize that the middle polarizer “prepares” a new polarization state that has components along the final analyzer’s axis.



====Links==== 
Three polarizing filters: a simple demo of a creepy quantum effect - Orion Lawlor: 
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3 Polarizing Filters - UMD Physics Videos!: 
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====Variations====
  * Use multiple intermediate polarizers at small angle steps to increase transmitted light through initially crossed polarizers.
  * Replace the 45° sheet with different angles (15°, 30°, 60°) and compare brightness.
  * Demonstrate polarization by reflection: view glare off a water tray through a rotatable polarizer, then relate to the filter axes used above.



====Safety Precautions====
  * Do not look directly into bright lamps or projectors; use a screen and indirect viewing.
  * Keep polarizing films away from hot projector vents to avoid warping.
  * Handle crystals and glass carefully to prevent cuts or chips.




====Questions to Consider====
  * Why do crossed polarizers with no intermediate sheet block nearly all light? (Their transmission axes are perpendicular, so a state prepared by the first has zero component along the second.)
  * How does the 45° sheet restore transmission between crossed polarizers? (It prepares a new linear state with nonzero components along both the first and the last axes; each stage transmits the component parallel to its axis.)
  * What does this teach about “state preparation” and “measurement”? (Each polarizer both measures the incoming polarization and prepares the outgoing state aligned with its axis.)
  * Would two photons ever interfere with one another in this setup? (No; the observed effects follow from each photon’s polarization state components and Malus’ law, not photon–photon interference.)