b
(b)Angle between \(P_1\) and \(P_2\) = \(30°\) (given)
Angle between \(P_2\) and \(P_3 = \theta = 90° -30° = 60°\)
The intensity of light transmitted by \(P_1\) is \({I_1} = \frac{{{I_0}}}{2} = \frac{{32}}{2} = 1\frac{W}{{{m^2}}}\)
According to Malus law the intensity of light transmitted by \(P_2\) is \({I_2} = {I_1}{\cos ^2}30^\circ = 16\,{\left( {\frac{{\sqrt 3 }}{2}} \right)^2} = 12\,\frac{W}{{{m^2}}}\)
Similarly intensity of light transmitted by \(P_3\) is \({I_3} = {I_2}{\cos ^2}\theta = 12{\cos ^2}60^\circ = 12\,{\left( {\frac{1}{2}} \right)^2} = 3\frac{W}{{{m^2}}}\)