Through Excel I obtained a calibration curve as shown in this figure
The equation of this curve is
$$y = 0,6209x^5 - 1,7958x^4 + 2,0116x^3 - 1,14x^2 + 0,3584x + 1,33$$
Now, through some experimental values of y (refractive index) I should go back to the value of x (molar fraction). Which formula should I use?
Thank you in advance
It won't be exactly the mathematical inverse of what you have, there, but I would just reverse the roles of $x$ and $y$ in a separate linear regression to get a reasonably good inverse function. Note: you might need to restrict the domain to ensure that the result is, indeed, a function.