Initially unpolarized light is sent through three polarizing sheets with transmission axes oriented at ${}_1=0^0,{}_2=30,$ and ${}_3=90$ measured counterclockwise from the $x-$axis.

Mathematical Analysis ${?}^{14}$

a$.$ What is the polarization direction of the exiting wave?

b$.$ What percentage of the initial intensity is transmitted by the system of the three sheets?

c$.$ Imagine rotating the polarization angle of the second sheet. To what angle should this polarizer be set to maximize the total transmission of the system?

d$.$ At the angle in $($c$),$ what percentage of the initial intensity is transmitted by the system?

e$.$ Imagine removing the second polarizing sheet. What happens to the transmitted intensity?

f$.$ Given that polarizers absorb light, carefully explain how it is possible to decrease the transmitted intensity by removing something that absorbs light.