$8\mathrm{.}1*$ Two light waves Ex $=$ E$0$ cos$($kz $-$ vt$)$ and Ey $=-$E$0$ cos$($kz $-$ vt$)$ overlap in space. Show that the resultant is linear light and determine its amplitude and tilt angle u$.8\mathrm{.}2*$ Two waves Ez $=4$ sin $($ky $-$ vt$)$ and Ex $=3$ sin $($ky $-$ vt$),$ both in SI units, overlap in space. Describe completely the state of polarization of the resultant. $8\mathrm{.}3*$ Consider the following two waves expressed in SI units: Ex $=8$ sin $($ky $-$ vt $+$ p$>2)$ and Ez $=8$ sin $($ky $-$ vt$).$ Which wave leads, and by how much? Describe the resultant wave. What is the value of its amplitude? $8\mathrm{.}4$ Describe completely the state of polarization of each of the following waves: $($a$)$ E$ $=$ i $$E$0$ cos$($kz $-$ vt$)-$ j $$E$0$ cos$($kz $-$ vt$)($b$)$ E$ $=$ i $$E$0$ sin $2$p$($z$>$l $-$ nt$)-$ j $$E$0$ sin $2$p$($z$>$l $-$ nt$)($c$)$ E$ $=$ i $$E$0$ sin $($vt $-$ kz$)+$ j $$E$0$ sin $($vt $-$ kz $-$ p$>4)($d$)$ E$ $=$ i $$E$0$ cos$($vt $-$ kz$)+$ j $$E$0$ cos$($vt $-$ kz $+$ p$>2).$