Recent content by H12504106

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...