Two sheets of polarizing material are placed with their...

Two sheets of polarizing material are placed with their transmission axes at right angles to one another. A third polarizing sheet is placed between them with its transmission axis at $45^{\circ}$ to the axes of the other two. (a) If unpolarized light of intensity $I_{0}$ is incident on the system, what is the intensity of the transmitted light?(b) What is the intensity of the transmitted light when

Key Concepts

Unpolarized Light

Unpolarized light consists of waves vibrating in multiple, randomly oriented planes. When such light encounters a polarizing material, the component of the light that aligns with the material’s transmission axis is selectively transmitted, resulting in a reduction in intensity. This is foundational to understanding how initial intensity is established before further polarization processes occur.

Polarizer

A polarizer is an optical filter that allows light waves of only a specific polarization to pass through while absorbing or reflecting the others. Polarizers are used to control the plane of polarization of light and play a crucial role in experiments and applications involving polarized light.

Malus' Law

Malus' Law quantifies the intensity of polarized light transmitted through an additional polarizer. The law states that the transmitted intensity is proportional to the cosine squared of the angle between the light’s initial polarization direction and the polarizer’s transmission axis. This principle is essential in calculating the intensity changes when light passes sequentially through multiple polarizing sheets.

Intermediate Polarizers

The insertion of an intermediate polarizer at an angle between two polarizers with perpendicular axes allows partial transmission of light that would otherwise be completely blocked. This phenomenon illustrates how the reorientation of the polarization plane by each polarizer can result in a non-zero transmitted intensity even when the first and last polarizers are orthogonal.

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