Unpolarized light passes through a succession of three po-...

Unpolarized light passes through a succession of three po- larizers. Their orientations with respect to the vertical are $0^{\circ}, 65^{\circ}$ and $45^{\circ}$, respectively. Find the fraction of the original light intensity remaining after each of the three polarizers.

Key Concepts

Unpolarized Light

Unpolarized light is composed of waves vibrating in all possible directions perpendicular to the direction of propagation. When such light interacts with a polarizing filter, only the component of the light that aligns with the filter’s orientation is transmitted, resulting in a reduction of intensity.

Polarizer

A polarizer is an optical filter that transmits light waves aligned with a specific polarization direction while absorbing or reflecting all other orientations. This directional selection transforms unpolarized light into polarized light, with an intensity reduction that depends on the alignment between the light's polarization and the filter's axis.

Malus's Law

Malus's Law quantitatively describes the intensity of polarized light after passing through a polarizer. It states that the transmitted light intensity is proportional to the cosine squared of the angle between the light's initial polarization direction and the axis of the polarizer, mathematically expressed as I = I? cos²?. This law is fundamental when analyzing the transmission of light through successive polarizers.

Successive Polarization

When light passes through multiple polarizers, each polarizer’s orientation relative to the polarization state of the incident light determines the transmitted intensity. The cumulative effect is calculated by applying Malus's Law at each step, with the light becoming re-polarized along each new polarizer’s axis. This concept is critical in designing optical systems where controlling light intensity and polarization is necessary.

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