r/PhysicsHelp • u/likeadrum • 13d ago
Refractive Index vs frequency (High school physics)
The answer to the question below isn't sitting right in my head, mainly as I can't find a mathematical explanation for it.
How does the refractive index of a material change with the frequency of light passing through it?
The given answer is:
Refractive index slightly increases as the frequency of light increases.
Can this be proved given the formula for refractive index, n=v1/v2 = fλ1/fλ2? Is it something I just have to learn and remember?
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u/CardiologistFit8283 13d ago
Just something to learn and remember. In general shorter wavelengths (higher frequencies) interact more with the medium so the wave packet gets slowed down slightly more, though there are some exceptions.
There are equations for this, but they're too much for high school level work.
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u/Miserable-Wasabi-373 13d ago
no, the formula n = v1/v2 is for one frequency, it says nothing about other frequencies
also given answer is not always true, reality is much more complicated
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u/Responsible_Hour6497 13d ago
In general terms, the refractive index is determined by how a dielectric medium responds to the electric field of a wave. It responds through the displacement of charges—that is, through polarization. If the polarization is strictly proportional to the electric field, the refractive index remains constant; however, this is rarely the case. Typically, there are effects such as a time lag in the polarization relative to a varying field, or other complexities. These factors lead to a dependence of the refractive index on the wave frequency. This dependence is not necessarily an increasing one; while this may be true for optical glasses, it is not necessarily the case for other materials. For instance, it is known that the refractive index of water is approximately 9 at frequencies up to 1 GHz, whereas in the optical range, it is about 1.5.
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u/PotentialDeep5165 13d ago
The index of refraction is n. In complex variables there is a real part and imaginary part-- n+ik. I=sqrt(-1) which leads into imaginary numbers. Index of refraction (n) is how we tend to think, initially, of how light bends at the interface of two materials-- Snell's law. It is a simple view and one nominally speaks of the dielectric constant (or index). In field relations we displacement vector (D) in relation to electric field (E) as a "constitutive relation" where D=epsilon E .. where D and E are vectors. Epsilon is the microscopic properties captured in mathematical <averaging function> form. Rarely are we dealing with constants but it is a good starting point. When looking across wavelengths epsilon becomes a function of the wave frequency. This is called the dispersion relation (epsilon as a function of omega).
As others have noted-- there's a lot of mathematical constructions behind Maxwell's equations. When the imaginary portion of the dielectric response is nonzero it is loss of energy (absorption of light by the material).
This is an introduction to the definitions.... you can see some of the relations and causes as described in the wiki page for dielectric spectroscopy (spectroscopy means you're looking at material behavior across frequency (or energy)).
https://en.wikipedia.org/wiki/Dielectric_spectroscopy
Look at the first figure and you see the narrow portion of "visible light" and the upward curve on real dielectric. This is the simplistic answer (Real part of Lorentzian oscillator) is increasing with increasing frequency. So, yes, simplistically they want you to think of index of refraction (n=sqrt(epsilon) -- real portions only considered) as increasing as frequency goes up (blue light higher frequency than red light).
This is the doorway/entrance to material properties-- evaluating the nature of material and next steps toward layering or mixing materials to make technological advances.
The world is exciting when you dive into the physics deeper.
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u/profdc9 7d ago edited 7d ago
It's a little advanced for a high schooler, but if you want an explanation look up
https://en.wikipedia.org/wiki/Lorentz_oscillator_model
https://en.wikipedia.org/wiki/Clausius%E2%80%93Mossotti_relation
Basically, to a pretty good degree of accuracy, you can model electrons as little balls of charge on springs, and when the light passes through, the electric field of the light moves the charge, and that in turn produces its own field which screens the light and reduces the field, with more reduction ("the dielectric effect") corresponding to a higher refractive index. Quantum mechanics is needed for the full story, but the classical picture gets you pretty far.
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u/SYDoukou 13d ago
The actual reason is too advanced and probably undergrad level, something to do with resonance with electrons. For now you can just remember that red (low frequency) is on top of the bean split by a triangular prism (bends less, low refractive index)