Why does dispersion increase with wavelength? If I understand correctly, refractive index is decreasing with wavelength. As a result, greater wavelengths are traveling faster. How does this cause the increase of dispersion?
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1$\begingroup$ You're not mixing wavelength and frequency? $\endgroup$– DakkVaderOct 4, 2018 at 10:36
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$\begingroup$ Also, does higher wavelength mean smaller refractive index for all materials? $\endgroup$– DakkVaderOct 4, 2018 at 10:38
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2 Answers
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It is not true that refractive index is a monotonic function of wavelength. A Google search will quickly show that nearly all materials have increasing refractive index with increasing wavelength in some parts of the spectrum, and decreasing in other parts. What matters is which side of a resonance you're on.
answered Oct 18, 2018 at 15:17
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Let's say you have a nice tight wave shape. Now decompose it into sine waves with a Fourier transform. Then let sine waves time-evolve: as you say different frequencies travel at different rates (in a dispersive medium).
When you at the later time add the sine waves back together (with an inverse Fourier transform), the wave packet is not so tight anymore. It has broaden, dispersed.
If all the sine waves traveled at the same speed, there would be no broadening, no dispersion.
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$\begingroup$ you are not clearly answering why some waves disperse more than others $\endgroup$ Oct 11, 2018 at 3:42