An unpolarized beam of light is sent into a stack of four...

An unpolarized beam of light is sent into a stack of four polarizing sheets, oriented so that the angle between the polarizing directions of adjacent sheets is $30^{\circ} .$ What fraction of the incident intensity is transmitted by the system?

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Key Concepts

Unpolarized Light

Unpolarized light consists of waves vibrating in all possible planes perpendicular to the direction of propagation. When unpolarized light encounters a polarizing filter, only the component of the light that aligns with the filter’s axis is transmitted, typically resulting in a transmitted intensity that is one half of the incident intensity.

Malus's Law

Malus's Law describes how the intensity of polarized light changes as it passes through a polarizer. Specifically, the transmitted intensity is given by the product of the incident intensity and the square of the cosine of the angle between the light's polarization direction and the polarizer’s axis. This law is essential for calculating the intensity after passing through each filter when their axes are at an angle relative to one another.

Sequential Polarization

In systems with multiple polarizing filters arranged at successive, small angles relative to one another, each filter rotates the polarization direction and reduces the intensity according to Malus's Law. This gradual rotation allows some light to be transmitted even through filters that are, in total, oriented at a large angle relative to the original polarization, illustrating the cumulative effects of sequential polarization.

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