Problem #$4(20$ pts$)$:

To design an anti$-$flare coating of a piece of glass, it requires the same type of coating is placed on both sides of the glass. The glass has a dielectric constant ${}_{rg}=6\mathrm{.}8.$ The light wave is normally incident on the glass.

a$)$ Calculate the intrinsic impedance of the glass ${}_g.$

b$)$ Without the coating, and assuming the glass is infinitely thick, what is the reflection coefficient seen looking into the glass?

c$)$ Draw the transmission line equivalent of the structure shown in the figure below.

d$)$ If the light wave has a frequency of $5\mathrm{.}24{10}^{14}Hz,$ how shall we select the dielectric constant ${}_{rc}$ and the thickness $d$ of the coating material to make the light pass through the glass without reflection? The thickness of the glass is arbitrary.

e$)$ After applying the coating you calculated in $($d$),$ what is the reflection coefficient looking into the coated glass? What is the impedance looking into the coated glass?