In Fig. 33-40, initially unpolarized light is sent into a...

In Fig. 33-40, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of $\theta_{1}=\theta_{2}=\theta_{3}=50^{\circ}$ with the direction of the $y$ axis. What percentage of the initial intensity is transmitted by the system? (Hint: Be careful with the angles.)

In Fig. 33-40, initially unpolarized light is sent into a system
of three polarizing sheets whose polarizing directions make angles of $\theta_{1}=\theta_{2}=\theta_{3}=50^{\circ}$ with the direction of the $y$ axis. What percentage of the initial intensity is transmitted by the system? (Hint: Be careful with the angles.)

Key Concepts

Polarization

Polarization refers to the direction in which the electric field oscillates in an electromagnetic wave. Unpolarized light contains waves oscillating in all directions perpendicular to the direction of propagation, and when it passes through a polarizing filter, it becomes polarized, meaning the light's oscillations are confined to a specific direction.

Polarizing Filters

A polarizing filter is a device that selectively transmits light waves oscillating in a certain direction while blocking others. When unpolarized light is incident on a polarizer, only the component of the light aligned with the filter’s axis is transmitted, and the intensity of the transmitted light is typically reduced.

Malus's Law

Malus's Law describes how the intensity of polarized light changes when it passes through a polarizing filter that is oriented at an angle to the beam's polarization direction. The law states that the transmitted intensity is proportional to the cosine squared of the angle between the light's polarization direction and the filter’s axis.

Angular Dependence in Multiple Polarizers

When light passes through multiple polarizing filters, each oriented at different angles, the transmitted intensity depends on the successive application of Malus's Law at each stage. The relative angles between the incoming polarization and each filter's axis determine the reduction in intensity, which must be carefully considered especially when the angles are not orthogonal.

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