Light Intensity from a Two-Polarizer Setup

To tease out the physical meaning of the state amplitudes in the equation $\ket{S} = a_{\text{h}}\ket{\text{hlp}} + a_{\text{v}}\ket{\text{vlp}}$, let’s use a polarizing sheet to produce a beam of linearly polarized photons. We then employ a PBS as a measurement device and measure how much of the linearly polarized light beam emerges in each of the PBS’s output beams. We then ask a critical question: what happens if we rotate the PBS relative to the polarization transmission axis of the polarizing sheet?

Cardy, how do you think the two intensities (the number of photons per second) will vary as we change the angle between the polarizing sheet and the PBS direction as shown in the figure below?