A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of I) of scattered light in the middle of the red part of the spectrum.

Verified step by step guidance

1. Understand the concept of Rayleigh scattering, which explains how light is scattered by particles much smaller than the wavelength of light. The intensity of scattered light is inversely proportional to the fourth power of the wavelength: \( I \propto \frac{1}{\lambda^4} \).
2. Identify the wavelengths for the green and red parts of the visible spectrum. Green light typically has a wavelength around 550 nm, while red light is around 650 nm.
3. Express the intensity of scattered light for green light as \( I_g \) and for red light as \( I_r \). Since \( I_g \propto \frac{1}{\lambda_g^4} \) and \( I_r \propto \frac{1}{\lambda_r^4} \), we can relate \( I_r \) to \( I_g \) using the ratio of their wavelengths.
4. Set up the equation for the intensity ratio: \( \frac{I_r}{I_g} = \left( \frac{\lambda_g}{\lambda_r} \right)^4 \). Substitute the known wavelengths for green and red light into this equation.
5. Solve the equation to express \( I_r \) in terms of \( I_g \). This will give you the intensity of scattered light in the middle of the red part of the spectrum in terms of the intensity \( I \) of the green part.

Key Concepts

Rayleigh Scattering

Rayleigh scattering is the scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. It is responsible for the blue color of the sky and explains why shorter wavelengths (like blue and green) scatter more than longer wavelengths (like red). The intensity of scattered light is inversely proportional to the fourth power of the wavelength.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that is visible to the human eye, ranging from approximately 380 nm to 750 nm. It includes colors from violet to red, with violet having the shortest wavelength and red the longest. Understanding the spectrum is crucial for analyzing how different wavelengths scatter differently.

Intensity of Light

Intensity of light refers to the power per unit area carried by a wave. In the context of scattering, it is the amount of light energy scattered in a particular direction. The intensity of scattered light depends on factors like the wavelength of the light and the size of the scattering particles, as described by Rayleigh's law.