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