Chapter 33: Problem 32
Three polarizing filters are stacked, with the polarizing axis of the second and third filters at 23.0\(^\circ\) and 62.0\(^\circ\), respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 55.0 \(\mathrm {W/cm}^2\) after it passes through the stack. If the incident intensity is kept constant but the second polarizer is removed, what is the intensity of the light after it has passed through the stack?
Short Answer
Step by step solution
Understand Polarization Concept
Initial Setup with Three Polarizers
Effect of the First Polarizer
Effect of the Second Polarizer
Effect of the Third Polarizer
Calculate Original Intensity \( I_0 \)
Remove Second Polarizer
Calculate New Intensity
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Malus's Law
- \( I \) is the resulting intensity of light after passing through the polarizer.
- \( I_0 \) represents the initial intensity of the polarized light.
- \( \theta \) denotes the angle between the light's initial polarization direction and the axis of the polarizer.
Unpolarized Light
- **First Polarizer:** The intensity drops to exactly half of its original value.
- **Subsequent Polarizers:** Further intensity reduction occurs according to Malus's Law as the angles between the polarizers' axes affect the intensity.
Light Intensity
- The first polarizer cuts the intensity in half because it filters out one plane of vibration.
- Each additional polarizer further modifies the light intensity following Malus's Law, reducing it depending on the angle between consecutive polarizers.