We have materials that have negative effective permittivity and permeability. In such materials, when the product of permittivity and permeability is negative, solving the wave equation yields a wave with a purely imaginary wave number. Does this mean complete attenuation of the wave ?
We can indeed take μ sin θ = constant for the whole path. But as I was saying, the next refraction that takes place inside the medium is through a surface that is perpendicular to the surface we had considered earlier (y = 0). This makes the angle to be considered different.
Even after we consider that the Snell's law holds, I still face problems drawing the path of the ray inside the medium. I am not sure of what has to be done inside the medium. It appears that the next refraction will be from a surface perpendicular to the plane we considered i.e. x = 0 if I...
I'm not quite sure about it. But if the ray strikes the surface at some point x = a, shouldn't the refractive index to be considered be the value μ = f(a) while applying Snell's law, if it is applicable.
Considering the setup in a plane might not be different. Still I'll clear it a bit. Here's an image.https://scontent-sin1-1.xx.fbcdn.net/hphotos-xaf1/v/t34.0-12/12167417_906070652794805_1640112228_n.jpg?oh=c670e33f48bae9df45946b176414dfe5&oe=5626B2E8
Consider an interface along x-axis which separates two media. The medium below y = 0 is air or vacuum and light is incident from this medium onto the surface. The refractive index of the medium above y = 0 varies with x as some function of x : μ = f(x). Does the Snell's law still hold good ??
If...