Light Beams through Multiple Polarizers

A polarizer (or polaroid) is a thin plastic sheet that produces a high degree of linear (or plane) polarization in light passing through it. This Demonstration shows a beam of unpolarized light reduced in intensity by 50% after passing through a polarizer oriented at an angle . (Angles are measured counterclockwise from the horizontal, looking into the beam from the screen.) A second polarizer oriented at angle will further reduce the intensity by a factor of . In particular, if the two polarizers are parallel (), there is no reduction in intensity. However, if the two polarizers are "crossed", with , no light will pass through.
A remarkable effect occurs when a third polarizer is inserted between two crossed polarizers: up to one quarter of the light intensity can then be transmitted. This is a consequence of the quantum nature of light. Photons linearly polarized at angle are transformed into a superposition of two linear polarizations parallel and perpendicular to a new angle with probabilities and , respectively.
In this Demonstration, you can observe the changes in intensity of a light beam as you vary the angles of two or three polarizers.

SNAPSHOTS

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DETAILS

Snapshot 1: parallel polarizers: full transmission of light beam
Snapshot 2: crossed polarizers: no transmitted light
Snapshot 3: insertion of third polarizer with intermediate orientation: some light gets through now! maximum when θ=45°
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