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We know that the Refractive Index is just a number that gives an idea of how much velocity of light decreases in comparison to vacuum. So, it makes sense to define a variable, n as:

n=c/v

where v is the velocity of light in that medium and say "well, this n thingy can't be less than 1 as speed of light is maximum in vaccum." So, if i were to change that ratio to something like:

n=v/c

and say that "well this n thingy can't be more than 1" then is that correct? what would change for the people studying physics if we started to use this?

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    $\begingroup$ Nature doesn't care about our definitions. What are you looking for in terms of what would change or go wrong? $\endgroup$ – BioPhysicist Oct 7 '19 at 4:09
  • $\begingroup$ no, of course, I didn't mean to say that "anything could go wrong" I was saying wrong as in for the people studying them. or more correctly, change. it would just change the calculations, right? $\endgroup$ – A N G E R Y Oct 7 '19 at 4:19
  • $\begingroup$ Welcome to Physics! Note that open-ended, hypothetical questions are explicitly off-topic. Please consider editing your post to have a more-specific question that can be answered. $\endgroup$ – Kyle Kanos Oct 8 '19 at 23:49
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All one would have to do is replace $n$ with $1\over n$ everywhere. Changing the definition will not affect the physics in any way.

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We can say "light travels in water 1.333 times slower than in vacuum", OR "light travels in water at $0.75c$". Both ways of describing speed of light in medium are valid. Besides more valid definitions of light speed in medium can be constructed, so what ? It changes nothing at all.

EDIT

Several alternative refractive index definitions:

  • $ n= \lambda_0 / \lambda $, based on wavelength in vacuum vs medium comparission
  • $ n = \frac{\sin(\alpha)}{\sin(\beta)} $, based on incident and refracted angles of light coming to material from vacuum (Snell's law)
  • $ n = \sqrt{\epsilon_r\mu_r}$, based on material's relative permittivity and permeability
  • $ n = \underline{n} - \kappa \space i$, based on complex refractive index and extinction coefficient

Many others refraction index definitions to be continued ... ! That's why Nature Laws are interesting and stable - you can arrive to the same material property or physical constant in many different ways !

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  • $\begingroup$ Any reason of down-vote ? $\endgroup$ – Agnius Vasiliauskas Oct 9 '19 at 6:00
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Our universe seems to tell a story that is independent of the words in which we have always chosen to express it. – Kate Becker

I like to shorten it down to: The world works the same, regardless of how we speak about it.

Mathematical formulations also count as a way of speaking about it. Math is a human invention - it is a "language" - that we use to describe our world. Talking about the world in English or German does not change how the world works. Describing the world in some mathematical terms or in other mathematical terms, doesn't change how the world works.

But naturally, if you speak in German, others who listen to you must be able to understand German. If you reinvent another mathematical description of some phenomenon, then you will only be able to talk about it with people who know about this other description. This other description might cause derived formulas and expressions to be different than we are used to as well - you are here altering the "language" that everyone are used to.

This might be fine. This might even be smart and useful, if it eases the work. Such as when tensor notation was introduced to easier describe vector and matrix relationships e.g. when dealing with fields and distributions, or such as when quantum bra-ket notation was introduced to describe quantum states more compressed. Everyone who already know math and physics just must then learn this new notation and this new version of the math "language".

(Adding new forms of notation in this manner is quite different from changing already existing and well-known formulas. You might need good reasons to do this to make it catch on.)

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