# Rayleigh Scattering calculation

• nmsurobert
In summary, the conversation discusses the concept of why the sky is blue and the difference between the "scattering" explanation found on the internet and the use of the I = 1/lambda^4 formula. The conversation also mentions a Wikipedia article with a more detailed equation that explains the blue color of the sky. The formula takes into account the incident wavelength and angle of the scattered light, and it is not a simplified version. The conversation also explains how the scattering of light in the atmosphere leads to the blue color of the sky and the red color of sunsets. Overall, the explanation for the blue color of the sky can be found in the scattering function.
nmsurobert
I've been trying to find a proof or a paper that goes into calculating why the sky is blue as opposed to the "the sky is blue because of scattering" explanation that all over the internet. I (think) understand the concept but I would like to see some numbers. I'm aware of the I = 1/lambda^4 formula. But I can't use that to explain the color of the sky. Is that a water down version of what is used to explain the color of the sky? I would think we have to take the incident wavelength into account as well as the size of the particle that causing the scattering.

Can anyone link me to something like this?

Thanks!

If you are aware of the formulas,
(for example see Wikipedia https://en.m.wikipedia.org/wiki/Rayleigh_scattering)
then I don’t think calculating is the issue. In particular equation six in the Wikipedia article shows the scattered intensity as a function of wavelength and angle and includes linked references if you’d like to see the derivation. That equation is not watered down, and it shows why the sky is blue.

Perhaps you would like some explanation as to what it means. When you look at the sky you are not looking at the sun. Light from the sun cannot go directly into your eye. Instead what you are seeing is sun light that was NOT traveling toward you. The light traveled directly from the sun to a point on a line along your line of sight. At that point it scattered from the atmosphere toward your eye. The line from the sun to the scatter point and the line from the scatter point to your eye make an angle. That is the scattering angle. Paths with multiple scatters are also happening, but the single scatter is much more probable. What the formula is telling you is that the probability of scattering (and therefore the scattered intensity) is much greater for shorter wavelengths (and smaller angles by the way) so the spectrum that reaches your eye is not white like sunlight, but weighted toward blue. For the very same reason reds are less likely to scatter and penetrate the atmosphere further making the light on the direct path a little yellow, or orange, or red depending on how much atmosphere it has to get through. That is why sunsets are red.

Bottom line, it is all right there in the scattering function.

anorlunda and nmsurobert
Awesome. I was looking for a derivation for the equation but if that's what it is then that's what it is. Thanks.

## What is Rayleigh scattering and why is it important?

Rayleigh scattering is a phenomenon where light is scattered by particles that are much smaller than the wavelength of the light. This is important because it is the reason why the sky appears blue and why the sun appears yellow during the day.

## How is Rayleigh scattering calculated?

Rayleigh scattering can be calculated using the Rayleigh scattering formula, which takes into account the wavelength of the light, the refractive index of the particle, and the size of the particle. This formula is based on the physics principles of scattering and wave interference.

## What factors affect the amount of Rayleigh scattering?

The amount of Rayleigh scattering is affected by the size and refractive index of the scattering particles, as well as the wavelength of the incident light. Additionally, the density and concentration of the particles in the medium can also impact the amount of scattering that occurs.

## What are some applications of Rayleigh scattering calculations?

One major application of Rayleigh scattering calculations is in atmospheric science, where it is used to study the composition and properties of the Earth's atmosphere. It is also used in remote sensing techniques to measure air pollution and other atmospheric conditions.

## How does Rayleigh scattering differ from Mie scattering?

Rayleigh scattering is a type of scattering that occurs when the size of the scattering particles is much smaller than the wavelength of the incident light. Mie scattering, on the other hand, occurs when the size of the particles is on the same order as the wavelength of the light. Mie scattering is commonly seen in larger particles, such as droplets in clouds, while Rayleigh scattering is more common in smaller particles, such as gas molecules in the atmosphere.

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