# Physical significance of Cauchy's constants?

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#1
Do they actually mean anything? My lab supervisor hinted that they do, but even after some thought I can't come up with anything.
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5 years ago
#2
(Original post by Sataris)
Do they actually mean anything? My lab supervisor hinted that they do, but even after some thought I can't come up with anything.
don't take my word but i think the reason as to why they mean anything is because the graph i exponential for refractive index and wavelength so mathematically there will always be more. However, in reality do we have that many different materials?

I'm not sure on the answer but this is what i would assume. Hope i gave some insight.
0
5 years ago
#3
(Original post by Sataris)
Do they actually mean anything? My lab supervisor hinted that they do, but even after some thought I can't come up with anything.
The answer is hidden in understanding how that incident electromagnetic wave propagates through the material:
Think about the mathematical expansion of that refractive index.

The Cauchy equation is a Fourier-Series expansion which lends itself to the analogy with waveform synthesis. i.e. a square wave can be synthesised from the summation of pure sinusoids starting with a fundamental frequency and then an infinite number of odd harmonics each of decaying amplitude as the harmonic number increases.

Ask yourself what is a refractive index and why the electro-magnetic wave frequency (wavelength) is important. i.e. why is the refractive index different for different materials and why it changes as the frequency changes? That will lead you to why each term in the Cauchy equation hints at the physical nature of atoms.

Big Hint: Think about the composition of atoms, electron excitation and decay and what happens as the wave front propagates through the material. i.e. why does the material refract the incident wave-front and how it propagates through the material?
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2 years ago
#4
Can't understand😖
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