optics - Relation between intensity of light and refractive index

The intensity of light (as calculated from time average of the poynting vector) is given by $I = (1/2) \epsilon v E_0^2$. Here the intensity is dependent on the velocity of light in the medium. The refractive index also depends on the velocity of light. So is it safe to say that the intensity of light depends on the refractive index of the medium?

Answer

Since $n=\sqrt{\varepsilon_r\mu_r}$ (the relative permeability $\mu_r$ being almost always $1$), and $v=\frac{c}{n}$, you can also write $I = \frac{nc\varepsilon_0}{2} E_0^2$. (We used the decomposition $\varepsilon=\varepsilon_r\varepsilon_0$.)

So, the intensity depends linearly on the refractive index.