What is the relation between Refractive index and speed of light?

What is the relation between Refractive index and speed of light?
State the relationship between wavelength of light and the size of the particle causing scattering?

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Intensity of scattered light is proportional to the fourth power of the wavelength of the incident light, provided the diameter of the scattering particle are smaller than the wavelength of the incident light.
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The scattered intensity is maximum for shorter wavelengths.