We present new high resolution and dynamic range dust column density and temperature maps of the California Molecular Cloud derived from a combination of Planck and Herschel dust-emission maps, and 2MASS NIR dust-extinction maps. We used these data to determine the ratio of the 2.2{mu}m extinction coefficient to the 850{mu}m opacity and found the value to be close to that found in similar studies of the Orion B and Perseus clouds but higher than that characterizing the Orion A cloud, indicating that variations in the fundamental optical properties of dust may exist between local clouds. We show that over a wide range of extinction, the column density probability distribution function (pdf) of the cloud can be well described by a simple power law (i.e., PDF_N_{prop.to}A_K_^-n^) with an index (n=4.0+/-0.1) that represents a steeper decline with A_K_ than found (n~=3) in similar studies of the Orion and Perseus clouds. Using only the protostellar population of the cloud and our extinction maps we investigate the Schmidt relation, that is, the relation between the protostellar surface density, {Sigma}_*_, and extinction, A_K_, within the cloud. We show that {Sigma}_*_ is directly proportional to the ratio of the protostellar and cloud pdfs, i.e., PDF_*_(A_K_)/PDF_N_(A_K_). We use the cumulative distribution of protostars to infer the functional forms for both {Sigma}_*_ and PDF_*_. We find that {Sigma}_*_ is best described by two power-law functions. At extinctions A_K_<=2.5mag, {Sigma}_*_{prop.to}A_K_^{beta}^ with {beta}=3.3 while at higher extinctions {beta}=2.5, both values steeper than those (~=2) found in other local giant molecular clouds (GMCs). We find that PDF_*_ is a declining function of extinction also best described by two power-laws whose behavior mirrors that of {Sigma}_*_. Our observations suggest that variations both in the slope of the Schmidt relation and in the sizes of the protostellar populations between GMCs are largely driven by variations in the slope, n, of PDF_N_(A_K_). This confirms earlier studies suggesting that cloud structure plays a major role in setting the global star formation rates in GMCs
