Two polarizing sheets, one directly above the other,...

Two polarizing sheets, one directly above the other, transmit $p \%$ of the initially unpolarized light that is perpendicularly incident on the top sheet. What is the angle between the polarizing directions of the two sheets?

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Key Concepts

Polarization

Polarization refers to the orientation of the oscillations of the electric field in a light wave. Light can be unpolarized, where oscillations occur in all directions perpendicular to the direction of propagation, or polarized, where the oscillations occur predominantly in one direction. Understanding polarization is key to analyzing how light behaves when interacting with polarizing filters.

Malus's Law

Malus’s Law quantifies the reduction in light intensity when polarized light passes through a second polarizer oriented at an angle to the light's polarization direction. It states that the transmitted intensity is proportional to the square of the cosine of the angle between the light’s polarization direction and the polarizer’s axis. This law is crucial for determining how much light is transmitted through multiple polarizing filters.

Transmission of Unpolarized Light Through a Polarizer

When unpolarized light encounters a polarizer, it becomes polarized along the axis of the filter, and its intensity is reduced by half because only the component of the light aligned with the filter's axis is transmitted. This initial transmission step is critical for setting up subsequent intensity calculations using Malus’s Law for additional polarizers.

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