In Fig. 33-42, unpolarized light is sent into a system of...

In Fig. $33-42,$ unpolarized light is sent into a system of three polarizing sheets. The angles $\theta_{1}, \theta_{2},$ and $\theta_{3}$ of the polariring directions are measured counterclock wise from the positive direction of the $y$ axis (they are not drawn to scale). Angles $\theta_{1}$ and $\theta_{1}$ are fixed, but angle $\theta_{2}$ can be varied. Figure $33-43$ gives the intensity of the light emerging from sheet 3 as a function of $\theta_{2}$. (The scale of the intensity axis is not indicated.) What percentage of the light's initial intensity is transmitted by the system when $\theta_{2}=30^{\circ} ?$

Key Concepts

Multiple Polarizer Transmission

In systems with more than one polarizer, the sequential application of Malus's Law at each stage determines the final intensity. Even if two polarizers are crossed (with their axes perpendicular), inserting an intermediate polarizer at a non-orthogonal angle can allow some light to be transmitted. The cumulative effect of these partial transmissions is crucial to understanding the overall intensity emerging from the system.

Malus's Law

Malus's Law quantifies the intensity of polarized light after passing through a polarizer, stating that the transmitted intensity is equal to the initial intensity times the square of the cosine of the angle between the light's polarization direction and the polarizer's axis. This law is fundamental in analyzing light intensity in systems with multiple polarizers.

Unpolarized Light

This refers to light whose electric field vectors oscillate in all directions perpendicular to the direction of propagation. Such light, when incident on a polarizer, emerges with a defined polarization direction and with its intensity reduced by half, because only the component aligned with the polarizer’s axis is transmitted.

Polarizing Filters

Polarizing filters are optical devices that allow light waves of a certain polarization to pass through while absorbing or reflecting others. Their orientation determines the direction of the transmitted light’s electric field, and when multiple filters are used, the relative angles between them critically influence the transmission intensity.

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