Answer
The intensity of the incident light is $65.7~W/m^2$
Work Step by Step
Let $I_0$ be the intensity of the incident light. Since the light is unpolarized initially, the intensity of the light after passing through the first polarizer is $\frac{I_0}{2}$
We can use the law of Malus to determine the intensity of the light after passing through the second polarizer.
$I_2 = \frac{I_0}{2}~cos^2(30.0^{\circ}) = \frac{3~I_0}{8}$
We can determine the intensity of the light after passing through the third polarizer.
$I_3 = \frac{3~I_0}{8}~cos^2(45.0^{\circ}-30.0^{\circ}) = 0.350~I_0$
We can find the intensity of the incident light:
$0.350~I_0 = 23.0~W/m^2$
$I_0 = \frac{23.0~W/m^2}{0.350}$
$I_0 = 65.7~W/m^2$
The intensity of the incident light is $65.7~W/m^2$
