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"Refractive index for air to glass is..." "Refractive index for glass to air is..."

Do these two statements make sense? I thought that the refractive index n is a constant for some material, but have never actually seen it expressed in terms of two materials except for in my textbook.

My textbook says that the refractive index for air to glass is the reciprocal of the refractive index for glass to air. But surely you can only have the refractive index of air or the refractive index of glass, but not from one to another?

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  • $\begingroup$ "I thought that the refractive index n is a constant for some material, but have never actually seen it expressed in terms of two materials except for in my textbook." - I agree with you. I don't think that the textbook worded their statement very well, either. $\endgroup$
    – user93237
    Commented Feb 19, 2018 at 19:23

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Usually the refractive index of a medium $1$ is defined by the ratio $$n_1=\frac {c}{c_1}$$ where $c_1$ is the phase velocity of light in the medium $1$, $c$ is the velocity of light in vacuum. You can also define a relative refractive index , $n_{21}$ of a medium $2$ relative to a medium $1$ by $$n_{21}=\frac {c_1}{c_2}=\frac {n_2}{n_1}$$ where $c_2$ is the phase velocity in medium $2$.

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  • $\begingroup$ Can n21 be a number less than 1? $\endgroup$
    – s.xw
    Commented Feb 19, 2018 at 19:41
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    $\begingroup$ @s.xw Of course, when $c_2 \gt c_1$. Even $n_1$ can be smaller than $1$ when the phase velocity $c_1$ in the medium $1$ is larger than the vacuum light velocity $c$. This happens e.g. in the frequency range of x-rays. $\endgroup$
    – freecharly
    Commented Feb 19, 2018 at 19:57

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