Homework Statement
A beam of light traveling in air hits a glass surface with refractive index 1.5 at 45 degree angle. The light is polarised at 45 degrees with respect to the plane of incidence. Calculate the polarization of the reflected beam. Homework Equations
Boundary Conditions...
Homework Statement
Consider an electromagnetic wave hitting a metallic surface with conductivity σ
at normal incidence.
a) Derive the wave equation describing this situation. Hint: Use Ohm’s law, J = σE to
eliminate the current.
b) Solve the wave equation for the electric field to...
Homework Statement
Let T be a linear operator on a finite dimensional vector space V. Suppose ||T(x)|| = ||x|| for all x in V, prove that T is one to one.
Homework Equations
||T(x)||^2 = <T(x),T(x)>
||x||^2 = <x,x>
The Attempt at a Solution
Suppose T(x) = T(y) x, y in V
Then...
Homework Statement
Let \sum_{n=1} a_n and \sum_{n=1} b_n be convergent series. For each n \in \mathbb{N}, let c_{2n-1} = a_n and c_{2n} = b_n. Prove that \sum_{n=1} c_n converges.
Homework Equations
The Attempt at a Solution
Not sure whether the following solution is...