Answer
Transmission of light through the system will be eliminated when $~~\theta = 20^{\circ}~~$ and $~~\theta = 90^{\circ}$
Work Step by Step
We can write an expression for the intensity of the light that is transmitted:
$I = I_0~cos^2~\theta$
Transmission of light through the system will be eliminated when the polarizing angles of sheet 2 and sheet 3 are at an angle of $90^{\circ}$ to each other.
The polarizing angle of sheet 2 is $0^{\circ}$
Therefore, transmission of light through the system will be eliminated when the polarizing angle of sheet 3 is $\theta = 90^{\circ}$
Transmission of light through the system will be eliminated when the polarizing angle of sheet 3 and sheet 4 are at an angle of $90^{\circ}$ to each other.
The polarizing angle of sheet 4 is $110^{\circ}$
Therefore, transmission of light through the system will be eliminated when the polarizing angle of sheet 3 is $\theta = 20^{\circ}$
Transmission of light through the system will be eliminated when $~~\theta = 20^{\circ}~~$ and $~~\theta = 90^{\circ}$
