In a $3-$D reference system, a dielectric material forming Region $1,$ where $lo{n}_1=8lo{n}_0,$ is on one side of a flat plane defined by $-3a_x+4a_z=15.$ On the other side of the plane, a second dielectric material forms Region $2$ where $lo{n}_2=5lo{n}_0.$ In Region $1,$ vec$(D_1)=-10\mathrm{.}0a_x-20\mathrm{.}0a_y+14\mathrm{.}0a_{z}C{m}^{-2}.$

Now, by stating any assumptions made, calculate

$($a$)$ Electric flux density, vec$(D_2).$

$($b$)$ Electric field intensity, vec$(E_2)$ expressed in terms of $lo{n}_0.$

$($c$),{}_1$ and ${}_2,$ the respective angles between the field vectors and the interface tangent.

$($d$)$ the ratio $\frac{cos{}_1}{cos{}_2}.$ Comment on its value.