Answer
a)
$C\lt A=B$.
b)
Case A: $I_2=9.25W/m^2$
Case B: $I_2=9.25W/m^2$
Case C: $I_2=0W/m^2$
Work Step by Step
(a) We know that the intensity of the first polarizer is given as
$I_1=I_{\circ}cos^2\theta_1$. Similarly, for the second polarizer, the intensity is given as $I_2=I_{\circ}cos^2\theta_1cos^2\theta_2$. Now, for case A and case B, the angle between the incident light and the transmission axis is the same and therefore, the intensity of the transmitted light in these two cases is the same. For case C, the angle between the incident light on the second polarizer and the transmission axis of the second polarizer is $90^{\circ}$. Thus, the intensity becomes zero in this case and we conclude that the order of the intensity of the transmitted light is $C\lt A=B$.
(b) We can find the intensity of the transmitted light for case A as follows:
$I_2=(37.0W/m^2)cos^2(45^{\circ})cos^2(45^{\circ})$
$\implies I_2=9.25W/m^2$
For case B:
$I_2=(37.0W/m^2)cos^2(45^{\circ})cos^2(45^{\circ})$
$\implies I_2=(37.0W/m^2)(0.5)(0.5)$
$\implies I_2=9.25W/m^2$
Now for case C:
$I_2=(37.0W/m^2)cos^2(45^{\circ})cos^2(90^{\circ})$
$\implies I_2=0W/m^2$
