I saw a video on how microwaving grapes make plasma. He said that the refractive index of microwave is about 10 inside the grape. Now, we don't know the wavelength of the microwaves in the grape or the velocity. We only know that it has a wavelength of about 12cm and frequency of about 2.45Ghz. Then how do we get the refractive index of microwaves in grapes as 10?
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As far as microwaves are concerned grapes are basically just water, and the refractive index for microwaves in water has been measured. For example a quick Google found me this report ($3.5$MB PDF)that studies the refractive index of water across a range of wavelengths from visible to radio. The relevant graph from the report is:
In the $1$ to $10$cm region the refractive index (the upper curve - the lower curve measures the absorption of the radiation) is actually nearer $9$ than $10$, but I imagine the author of the video chose $10$ as nice round number.
Googling for the microwave refractive index of grapes returned many amusing but irrelevant hits, but also the paper Linking plasma formation in grapes to microwave resonances of aqueous dimers, which looks as if it goes into considerable detail on the subject.
answered Feb 26, 2019 at 15:45
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$\begingroup$ can you give me a formula at BSc level so I can calculate it on my own? $\endgroup$– user167524Commented Feb 26, 2019 at 15:55
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1$\begingroup$ @Korra no, I'm afraid not. The refractive index is related to the strength of the interaction between the oscillating electric field of the EM wave and the electrons in the dielectric. This is fearsomely difficult to calculate from first principles, so in practice we use experimental measurements and fit curves to these. The report I linked describes this, though as it happens in the microwave region the real art of the refractive index just has the constant value of $9$. $\endgroup$ Commented Feb 26, 2019 at 15:59