Visualizing the dielectric profile between a conductor and an dielectric during wave equation derivation

I was deriving the wave equation for a conductor and a dielectric medium. While solving it considered the dielectric constant with negligible variation over distances on the order of one optical wavelength shown below as follows:

$$epsilon =epsilon(r) $$

After this they construct the following equation:

$$nabla^2 E-(epsilon/c^2)frac{partial^2 E }{partial t^2}=0$$

Can anyone please explain how the profile is developed or constructed?
Can we also have a graphical understanding of the assumption here??