A beam of unpolarized light of intensity I0 passes through a...

A beam of unpolarized light of intensity $I_0$ passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in $\textbf{Fig. E33.27}$. (a) What is the light intensity (in terms of $I_0$) at points $A$, $B$, and $C$ ? (b) If we remove the middle filter, what will be the light intensity at point $C$ ?

Key Concepts

Effect of Removing a Polarizer

Removing one polarizer from a series of rotated polarizers alters the cumulative polarization transformation and typically results in a different final intensity. Without the intermediate filter, the light does not have the gradual reorientation and may undergo a more significant intensity loss when confronted with a larger angular misalignment, according to Malus's Law.

Sequential Polarization and Intermediate Filters

Using multiple polarizers in series can gradually rotate the polarization direction of the light. An intermediate polarizer between two polarizers with a large angular difference can reduce the overall loss of intensity by orienting the light more favorably for the final polarizer. This technique demonstrates that even if the first and last polarizers are oriented perpendicularly, the introduction of an intermediate polarizer can allow some light to be transmitted through the system.

Unpolarized Light

Unpolarized light consists of waves vibrating in all possible directions perpendicular to the direction of propagation. When unpolarized light passes through a polarizer, only the component of the light that aligns with the filter’s transmission axis is allowed through, resulting in a reduction of light intensity.

Ideal Polarizing Filter

An ideal polarizing filter transmits light that is polarized along its transmission axis and completely blocks the component perpendicular to it. For unpolarized light, this means that at the first filter the transmitted intensity is reduced to one-half of the incident intensity, setting the stage for further intensity adjustments in subsequent filters.

Malus's Law

Malus's Law states that when polarized light of intensity I? passes through a second polarizer, the transmitted intensity I is given by I = I? cos²?, where ? is the angle between the light’s polarization direction and the axis of the second polarizer. This law explains how each rotated filter further reduces the transmitted intensity based on the relative orientation of the polarizers.

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