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Homework Statement
The electric field of an electromagnetic wave traveling in the dielectric can be written as
E = (E0) e(iωt−ikx)
where E0 is a constant vector and |k| = [ω(ε)^1/2]/c .
Consider an electromagnetic wave traveling in vacuum towards the dielectric at an angle θ
to the x-axis with its electric field polarised in the x, y plane. When this wave is incident
on the dielectric a scattered wave and a transmitted wave are produced.
By imposing the relevant boundary conditions on the electric field across the boundary, or
otherwise, derive Snell’s law.
Homework Equations
Snell's law : (sinθ1)(n1)=(sinθ2)(n2)
Where:
θ1 is the angle of incidence and θ2 is the angle of reflection,measured with respect to the normal.
n is the refractive index of the material
n1,2 = velocity of light in a vacuum / velocity of light in medium
ω=2πu=ku
where :
k is the wave number defined as:
λ=2π/k
ω is the angular frequency
u is the frequency