Unpolarized light is incident on a system of three...

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of $30.0^{\circ}$ with respect to the first and the third is oriented at an angle of $45.0^{\circ}$ with respect to the first. If the light that emerges from the system has an intensity of $23.0 \mathrm{W} / \mathrm{m}^{2},$ what is the intensity of the incident light?

Key Concepts

Polarization

Polarization refers to the orientation of the oscillations of the electromagnetic field in light. In unpolarized light, these oscillations occur in all directions perpendicular to the direction of propagation, while in polarized light the oscillations occur predominantly in one direction. This concept is fundamental to understanding how polarizers work to filter light according to its orientation.

Unpolarized Light

Unpolarized light has electric field vectors that oscillate in random directions. When unpolarized light passes through a polarizer, only the component of the light aligned with the polarizer’s axis is transmitted, effectively reducing its intensity by half, which is a key aspect to consider in problems involving light intensity calculations through polarizing filters.

Polarizer

A polarizer is an optical filter that allows light waves of a certain polarization to pass through while blocking waves of other polarizations. The orientation of the polarizer's transmission axis determines which component of the light is transmitted. Understanding the function of a polarizer is essential when analyzing systems where multiple polarizers are used, as it affects the intensity of transmitted light.

Malus' Law

Malus' Law quantitatively describes the intensity of polarized light after it passes through a polarizer. It states that the transmitted intensity is proportional to the square of the cosine of the angle between the light's initial polarization direction and the polarizer's transmission axis. This law is crucial when calculating how much light is transmitted through successive polarizers with different orientations.

Multiple Polarizer Systems

A system involving multiple polarizers requires sequential application of polarization principles and Malus' Law. Each polarizer alters the light's polarization state and intensity. By considering the relative angles between successive polarizers, one can determine the cumulative effect on the light's intensity, which is a common problem in the analysis of optical systems.

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