Randomly polarized light with intensity I0 passes through...

Randomly polarized light with intensity $I_{0}$ passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles $\theta_{1}$ and $\theta_{2}$, respectively, to the horizontal. Rank the intensities of the light transmitted through the second polarizer, from greatest to least. (a) $\theta_{1}=0^{\circ}, \theta_{2}=30^{\circ}$ (b) $\theta_{1}=30^{\circ}, \theta_{2}=30^{\circ}$ (c) $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$ (d) $\theta_{1}=60^{\circ}$ $\theta_{2}=0^{\circ} ;$ (e) $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ}$.

Randomly polarized light with intensity $I_{0}$ passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles $\theta_{1}$ and $\theta_{2}$, respectively, to the horizontal. Rank the intensities of the light transmitted through the second polarizer, from greatest to least.
(a) $\theta_{1}=0^{\circ}, \theta_{2}=30^{\circ}$
(b) $\theta_{1}=30^{\circ}, \theta_{2}=30^{\circ}$
(c) $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$
(d) $\theta_{1}=60^{\circ}$
$\theta_{2}=0^{\circ} ;$ (e) $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ}$.

Key Concepts

Intensity Transmission Through Multiple Polarizers

When light passes through multiple polarizers, its intensity is progressively reduced. For unpolarized light, the first polarizer typically reduces the intensity by half and polarizes the light; subsequent polarizers then further reduce the intensity according to Malus' Law. The relative angles between the successive polarizers’ transmission axes determine the final transmitted light intensity, making it important to understand how these angles affect the cosine-squared reduction in intensity.

Malus' Law

Malus' Law quantifies the intensity of polarized light after it passes through an ideal polarizing filter. According to this law, the transmitted light intensity is proportional to the square of the cosine of the angle between the light’s initial polarization direction and the transmission axis of the polarizer. This principle is crucial when calculating the intensity of light after passing through successive polarizers with different orientations.

Polarization

Polarization refers to the orientation of the oscillations of the electromagnetic wave’s electric field vector. In many optical phenomena, the behavior of light depends on its polarization state—whether it is randomly oriented (unpolarized) or has a specific orientation (polarized). This concept is fundamental in understanding how various optical devices, such as polarizers, affect the propagation and intensity of light.

Polarizers

Polarizers are optical devices that allow only light waves oscillating in a particular direction to pass through while blocking waves in other directions. They are key tools in controlling and filtering light based on its polarization, and their orientation (transmission axis) determines the specific direction of light they transmit. Understanding their function is essential when analyzing how multiple polarizers interact with incident light.

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