Problem $8$: $(9\%$ of Assignment Value$)$

Linearly polarized light is transmitted through two polarizers as shown in the figure. The light is polarized in the $y$ direction. The axis of the first polarizer is at ${}_1=26$ to the $y$ direction. The axis of the second polarizer is at ${}_2=58$ to the $y$ direction. The intensity of the initial beam of polarized light is $I_0.$

Part $($a$)$

Express the intensity of the light after it passes through the first polarizer, $I_1,$ in terms of $I_0,$ and ${}_1.$

$I_1=$

$$

$\backslash$table$[[cos(),cos({}_{21}),cos(),,7,9,$HOME$],[cos(),cos({}_1),sin(),{?}^{?},($i$)45,6,],[sin({}_{21}),sin(),sin(),,12,3,$