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 (a) the red part of the spectrum.

Verified step by step guidance

1. Understand the concept of Rayleigh scattering, which explains that the intensity of scattered light is inversely proportional to the fourth power of the wavelength. This means that shorter wavelengths scatter more intensely than longer wavelengths.
2. Identify the wavelengths for the green and red parts of the visible spectrum. Typically, green light is around 550 nm and red light is around 700 nm.
3. Set up the ratio of the intensities of scattered light using the Rayleigh scattering formula: \( I_{\text{red}} = I_{\text{green}} \left( \frac{\lambda_{\text{green}}}{\lambda_{\text{red}}} \right)^4 \).
4. Substitute the wavelengths of green and red light into the formula to find the ratio of \( I_{\text{red}} \) to \( I_{\text{green}} \).
5. Simplify the expression to find the intensity of the red light in terms of \( I \), the intensity of the green light.

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. This phenomenon explains why shorter wavelengths (blue and violet light) scatter more than longer wavelengths (red light), leading to the blue color of the sky. In the context of the question, it helps understand why the intensity of scattered light varies across different colors in the spectrum.

Visible Spectrum

The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye, typically ranging from about 380 nm (violet) to 750 nm (red). Each color within this spectrum corresponds to a specific wavelength, with red light having the longest wavelength. Understanding the visible spectrum is crucial for analyzing how different colors of light are scattered and perceived.

Intensity of Light

The intensity of light refers to the power per unit area carried by a wave, which is perceived as brightness. In scattering phenomena, the intensity of scattered light can vary based on the wavelength of the incident light and the scattering mechanism involved. In this question, the intensity of scattered light in the red part of the spectrum can be derived from the intensity in the green part by applying the principles of scattering.