Wave equation in inhomogeneous media -- Question about the formula

[macabre]

https://i.hizliresim.com/ZO0bvG.jpg

I don't understand that where ε0/ε is coming from? Can you explain this?

 

[Paul Colby]

Well, the first equation is,

$\nabla \times H = \frac{\partial D}{\partial t}$

to which we note, $D = \epsilon(r)E$ to get,

$\frac{1}{\epsilon(r)}\nabla \times H = \frac{\partial E}{\partial t}$

so,

$\nabla\times[\frac{1}{\epsilon(r)}(\nabla\times H)] = -\mu_o \frac{\partial^2 H}{\partial^2 t}$

where we've snuck in $B=\mu_o H$. Multiply both sides by $\epsilon_o$ and note that $\epsilon_o \mu_o = \frac{1}{c^2}$

 

[macabre]

Thank you