$(10$ points$)($a$)$ Consider incoming light with intensity $I_0$ incident on a polarizer. How much light $I_1$ is transmitted in terms of $I_0?$

$($b$)$ If a second polarizer is at an angle ${}_1$ relative to the first, how much light $I_2$ is transmitted in terms of $I_0?$

$($c$)$ Now let's add a third at angle ${}_2$ relative to the second polarizer. How much light is now transmitted in terms of $I_0?$

$($d$)$ What are each of these numerically for $I_0=1025\frac{J}{m^2*(s)},{}_1=30,{}_2=20?$