Rayleight scattering derivation

In summary, the conversation discusses a problem with understanding the derivation of equation 5.82 in a textbook on Optical Waveguide Theory. The speaker has attempted to use the instructions and equations 5.79, 5.80, and 5.81, but has been unable to obtain the desired outcome. They are seeking assistance in understanding how equation 5.82 is derived.
  • #1
NeicKosir
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Homework Statement


I have a problem understanding derivation of particular equation in a textbook on Optical Waveguide Theory (Snyder, Love) - see attached.

The equation 5.79 is the starting point. Explanation of 5-80 are clear and derivation of 5-81 likewise. I am stuck, however with 5-82, which i can't see how was obtained. I have followed the instructions, but it does not come together.

Homework Equations


Does someone see how the 5-82 is obtained? Or there is some good portion of data missing?

The Attempt at a Solution

 

Attachments

  • Scanned_20151102-0645.pdf
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  • #2
I have tried to plug the expression for B from 5-81 into 5-80, which did not result in the desired outcome. I have also tried to multiply the expression for B in 5-81 by itself, but got stuck.
 

1. What is Rayleigh scattering?

Rayleigh scattering is a phenomenon in which light is scattered by particles in the atmosphere or other transparent materials, causing the light to change direction and resulting in the blue color of the sky.

2. How does Rayleigh scattering work?

Rayleigh scattering occurs when light passes through a medium and encounters particles that are much smaller in size than the wavelength of the light. The particles absorb and re-emit the light, causing it to scatter in all directions.

3. What is the mathematical formula for Rayleigh scattering?

The mathematical formula for Rayleigh scattering is given by the Rayleigh scattering cross section, which is proportional to the fourth power of the wavelength of the light and inversely proportional to the fourth power of the particle size.

4. What are the applications of Rayleigh scattering?

Rayleigh scattering has various applications in atmospheric science, including measuring air pollution and monitoring climate change. It is also used in optical communication and remote sensing technologies.

5. How is Rayleigh scattering related to the color of the sky?

Rayleigh scattering is responsible for the blue color of the sky during the day. This is because blue light has a shorter wavelength and is scattered more easily by the particles in the atmosphere, while longer wavelength colors like red and orange are less affected and are able to pass through the atmosphere with less scattering.

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