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. If we remove the middle filter, what will be the light intensity at point C?

Verified step by step guidance

1. Understand that unpolarized light has an equal intensity in all directions. When it passes through a polarizing filter, the intensity is reduced to half of the original intensity, I0. This is because the filter only allows light waves oscillating in one direction to pass through.
2. Recall Malus's Law, which states that when polarized light passes through a second polarizing filter, the intensity of the light is given by: $I=I$₀⁢cos2θ, where $\theta$ is the angle between the light's polarization direction and the filter's axis.
3. Consider the scenario where the middle filter is removed. Initially, the unpolarized light passes through the first filter, reducing its intensity to $\frac{I}{}$₀2.
4. After passing through the first filter, the light is polarized. When this polarized light reaches the last filter, apply Malus's Law again. The intensity at point C will be determined by the angle between the polarization direction of the light after the first filter and the axis of the last filter.
5. Calculate the final intensity at point C using Malus's Law: $I=\frac{I}{}$₀2⁢cos2θ, where $\theta$ is the angle between the polarization direction after the first filter and the axis of the last filter.

Key Concepts

Unpolarized Light

Unpolarized light consists of waves vibrating in multiple planes perpendicular to the direction of propagation. When such light passes through a polarizing filter, it becomes polarized, meaning it vibrates in a single plane. Understanding this transformation is crucial for analyzing how light intensity changes through polarizing filters.

Malus's Law

Malus's Law describes how the intensity of polarized light changes as it passes through a polarizing filter. The intensity I of light after passing through a filter is given by I = I0 * cos²(θ), where I0 is the initial intensity and θ is the angle between the light's polarization direction and the filter's axis. This law is essential for calculating the intensity at point C after removing the middle filter.

Polarizing Filters

Polarizing filters allow light waves vibrating in a specific direction to pass through while blocking others. When multiple filters are used, the orientation of each filter's axis relative to the previous one affects the resultant light intensity. Understanding how these filters interact is key to determining the final intensity at point C when the middle filter is removed.