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Chapter 9: Problem 59

Water droplets in clouds scatter sunlight similar to the way air molecules do. Since clouds are white (during the day), what can you conclude about the frequency dependence of scattering by cloud particles?

Short Answer

Expert verified
Answer: The main difference between Rayleigh scattering and scattering by cloud particles in terms of frequency dependence is that Rayleigh scattering has an inverse fourth-power dependence on the wavelength, scattering shorter wavelengths more than longer wavelengths. In contrast, the scattering by cloud particles has a weaker frequency dependence, causing all visible wavelengths to scatter similarly and creating the white appearance of clouds during the day.

Step by step solution

01

Understand the concept of Rayleigh scattering

Rayleigh scattering is the elastic scattering of light by particles much smaller than the wavelength of light. This phenomenon is responsible for the blue color of the sky and the red color of the sun during sunsets. The intensity of scattered light depends on the size of the particles and the wavelength of the incident light.
02

Recall the Rayleigh scattering equation

The intensity of light scattered by particles in the Rayleigh scattering regime is given by the equation: I(λ) ∝ (1/λ^4) * N * (d^6 * π^5 * n^2) / (3 * k) where I(λ) is the intensity of scattered light as a function of the wavelength (λ), N is the number of particles per unit volume, d is the diameter of the particles, n is the refractive index of the particles, k is the Boltzmann constant In the Rayleigh scattering regime, the intensity of scattered light is inversely proportional to the fourth power of the wavelength of incident light. This means that shorter wavelengths (blue light) will scatter more than longer wavelengths (red light).
03

Analyze the scattering by cloud particles

Clouds are made up of water droplets with a typical size range of about 10 micrometers to 100 micrometers in diameter. It is larger than the wavelengths of visible light (about 400 nm to 700 nm), so the scattering by cloud particles doesn't follow Rayleigh scattering strictly. However, it is still informative to discuss the frequency dependence based on Rayleigh scattering to grasp the main idea. Since clouds appear white, it means that all visible wavelengths are being scattered similarly. In Rayleigh scattering, shorter wavelengths are scattered more than longer wavelengths. For the clouds to appear white, this frequency dependence must be decreased or even canceled out.
04

Conclude on the frequency dependence of scattering by cloud particles

Based on the analysis, we can conclude that the frequency dependence of scattering by cloud particles is weaker than the inverse fourth-power dependence observed in Rayleigh scattering. As a result, the scattering by cloud particles doesn't favor one wavelength over another, causing all visible wavelengths to scatter similarly and creating the white appearance of clouds during the day.

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