# What is meant by the refractive index for $X$ to $Y$?

"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?

• "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. – Samuel Weir Feb 19 '18 at 19:23

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 $2$.
• @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. – freecharly Feb 19 '18 at 19:57