Two polarizing filters are crossed at 90^∘, so when light is shined from behind the pair of filt

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Two polarizing filters are crossed at 90^∘, so when light is...

Two polarizing filters are crossed at $90^{\circ}$, so when light is shined from behind the pair of filters, no light passes through. A third filter is inserted between the two, initially aligned with one of them. Describe what happens as the intermediate filter is rotated through an angle of $360^{\circ}$

Key Concepts

Polarization

Polarization refers to the orientation of the oscillations of a light wave perpendicular to its direction of travel. In unpolarized light, the electromagnetic vibrations occur in all possible directions, while polarizing filters select light oscillating in a single plane, aligning its polarization to a specific direction.

Polarizing Filters

Polarizing filters are optical devices that allow only light waves with a certain polarization direction to pass through. When light passes through a polarizer, its electric field components that are aligned with the filter's transmission axis are transmitted, while components perpendicular to this axis are absorbed or reflected.

Malus's Law

Malus's Law is a mathematical relationship that describes how the intensity of light changes as it passes through a polarizing filter. It states that the transmitted intensity is proportional to the cosine squared of the angle between the light’s polarization direction and the transmission axis of the filter. This law is key when analyzing cases where polarizers are rotated relative to one another.

Intermediate Filter Insertion in Crossed Polarizers

When a third, intermediate polarizing filter is inserted between two crossed polarizers (which are oriented at 90° to each other), the intermediate filter’s orientation introduces a component of the light’s polarization that can pass through the second polarizer. As this intermediate filter is rotated through 360°, it modulates the projection of the light’s polarization onto the final filter’s axis, resulting in varying light intensities despite the originally crossed configuration.

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