too short to permit Cherenkov imaging in a very large detector. The optical attenuation length of more recent WbLS formulations has been improved by about 2 orders of magnitude (figure \[fig:UVVIS\]). To first order, the fraction of absorbed Cherenkov photons simply scales with the optical attenuation length, which suggests that the $\approx 58\%$ loss of Cherenkov photons would occur over a path length of ${\mathcal O}(10 {\rm m})$ using the more recent WbLS formulation; which is a length scale suitable for a large detector. Experimental measurements in a larger detector geometry are needed to more rigorously assess this model prediction.

Our measurements can also give an estimate of the relative proportions of measured WLS and scintillation photons. The mean number of photons detected in the upstream PMT of Detector A for 2 GeV protons incident on WbLS-2 may be written as the sum of the detected scintillation and WLS light components: $$N_{up}(WbLS, 2~GeV) =   N_{up}^{Scint}(WbLS, 2~GeV) + N_{up}^{WLS(Ckov)}(WbLS, 2~GeV)
\label{eqn:Up2GeV}$$ where $N_{up}^{Scint}(WbLS, 2~GeV)$ and $N_{up}^{WLS(Ckov)}(WbLS, 2~GeV)$ are the mean number of detected scintillation photons and WLS Cherenkov photons, respectively. Any wavelength shifting of scintillation light is disregarded in this approximation.

The mean number of photons detected in the upstream PMT 