#$2-$ Wave Equation and Polarization: This question has multiple, mostly unrelated parts.

a$.$ An electromagnetic wave will have electric and magnetic fields of the forms in equations $(1)$ and $(2),$

that both satisfy the modified version of Faraday's Law that we derived in class $(3).$ Use these equations

to prove the equation shown in class which relates the magnitudes of the electric and magnetic fields in

an electromagnetic wave: E$\_(0)=$cB$\_(0).$

$(1)$ E$=$E$\_(0)$cos$($kx$-\backslash$omega t$)$

$(2)$ B$=$B$\_(0)$cos$($kx$-\backslash$omega t$)$

$(3)($delE$)/($delx$)=-($delB$)/($delt$)$

b$.$ A red light laser $(\backslash$lambda $=680$nm$)$ shines coherent light $($meaning all the light emitted has the same phase

constant$)$ with a phase constant of $\backslash$phi $\_(0)=0.$ If the amplitude of the wave's electric field E$\_(0)$ is $80($V$)/($m$),$

find the magnitude of the electric and magnetic fields at the source at t$=1$ nanosecond.

c$.$ Write a few sentences to explain how one might use polarizing filters to create an adjustable light filter

$($that you can easily adjust to make the light brighter or dimmer$)$ for sunlight $($which is naturally

unpolarized$).$ Be specific about the number of filters you would use, how they would be placed, and how

you would adjust the transparency of the filter.