A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in Fig. E33.27. (b) If we remove the middle filter, what will be the light intensity at point C?

Verified step by step guidance

1. Identify the initial intensity of the unpolarized light, which is given as I0.
2. Understand that when unpolarized light passes through a polarizer, the intensity of the light is reduced by half. Therefore, after passing through the first polarizer, the intensity becomes I0/2.
3. Recognize that the middle polarizer, which is now removed, would have further affected the intensity based on its angle relative to the first polarizer. However, since it is removed, this step is skipped.
4. Consider the effect of the final polarizer. Since the middle polarizer is removed, the angle between the first and the final polarizer becomes the relevant factor. Use Malus's Law, which states that the intensity I after passing through a polarizer is given by I = I_initial * cos^2(θ), where θ is the angle between the initial polarization direction and the polarizer axis.
5. Calculate the final intensity at point C using the angle between the first and the final polarizer and the intensity from the first polarizer, which is I0/2.

Key Concepts

Malus's Law

Malus's Law states that when polarized light passes through a polarizing filter, the intensity of the transmitted light (I) is given by I = I0 * cos²(θ), where I0 is the intensity of the incoming light and θ is the angle between the light's polarization direction and the filter's axis. This principle is crucial for understanding how light intensity changes as it passes through multiple polarizers.

Unpolarized Light

Unpolarized light consists of waves vibrating in multiple planes perpendicular to the direction of propagation. When unpolarized light passes through a polarizing filter, it becomes polarized, with its waves aligned along the filter's axis. This transformation is essential for analyzing how the intensity of light changes as it interacts with polarizing filters.

Series of Polarizers

When multiple polarizing filters are arranged in series, the intensity of light passing through them is affected by the orientation of each filter. The first filter polarizes the light, and subsequent filters further modify the intensity based on their angles relative to the previous filter. Understanding this series effect is key to determining the final intensity of light at a given point after passing through multiple filters.