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Correct Answer: malus’ s law
the relationship between a polarizer and an analyzer in an optical system is fundamentally described by malus's law. this law, which is critical in the study of optics, explains how the intensity of light passing through a polarizing filter changes depending on the angle between the polarizer and the analyzer.
to understand this relationship, consider first a polarizer which aligns light waves to vibrate in a single plane. when unpolarized light (light vibrating in all planes perpendicular to the direction of travel) enters a polarizer, the device blocks all light waves except those vibrating parallel to its axis. the light that emerges is thus polarized.
following the polarizer, if we place another polarizing filter called an analyzer, the intensity of the initially polarized light that passes through this second filter will depend on the angle between the axes of the polarizer and the analyzer. this is where malus's law comes into play.
malus's law states that the intensity \( i \) of polarized light after passing through the analyzer is given by the equation:
\[
i = i_0 \cos^2 \theta
\]
where \( i_0 \) is the intensity of the polarized light after it has passed through the polarizer (but before the analyzer), and \( \theta \) is the angle between the polarization axis of the polarizer and the analyzer.
when \( \theta = 0^\circ \) (i.e., the axes of the polarizer and analyzer are aligned), \( \cos^2 \theta = 1 \), and the intensity of the light is not reduced by the analyzer, \( i = i_0 \). conversely, when \( \theta = 90^\circ \) (i.e., the axes are perpendicular), \( \cos^2 \theta = 0 \), and the light's intensity becomes zero after the analyzer, effectively blocking all the light.
in essence, malus's law quantitatively describes how the angle between a polarizer and an analyzer affects the transmission of light, which is pivotal in applications ranging from photography to the study of light behavior in various media. this fundamental optical principle has wide-reaching implications in both scientific research and various technological applications.
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