$1.(20$ Marks$)$ Four polarizing sheets are stacked as follows: the first is at $40\mathrm{.}0$ clockwise $($CW$)$ with the vertical, the second is horizontal, the third is at an angle of $70\mathrm{.}0$ CW with the vertical and the fourth is vertical

What fraction of the incident light is transmitted by this system if

a$)$ the incident light lo is wepolarized!

b$)$ the incident light lo is horizontally polarized?

For the remainder of the problem assume that Is $600$ W$/$m$^2$ and is vertically polarized.

c$)$ Calculate the transmitted intensity if the second polarizer is removed.

d$)$ What would be the transmitted intensity if the second and the third polarizer are exchanged?

e$)$ If the fourth polarizer is removed, what should be the angle $($with the vertical$)$ of the second polarizer so that maximum intensity can be transmitted through the system? Calculate this maximum intensity

f

$)$ Light is incident on air water interface at the Brewster angle $8$ of that interface und reflects toward the original system of $4$ polarizers. Calculate the transmitted intensity$$by$$the