We evaluate the logarithmic derivative of the depth of the solar convective zone with respect to the logarithm of the radiative opacity , \partial \ln R _ { CZ } / \partial \ln \kappa .
We use this expression to show that the radiative opacity near the base of the solar convective zone ( CZ ) must be known to an accuracy of \pm 1 % in order to calculate the CZ depth to the accuracy of the helioseismological measurement , R _ { CZ } = ( 0.713 \pm 0.001 ) R _ { \odot } .
The radiative opacity near the base of the CZ that is obtained from OPAL tables must be increased by \sim 21 % in the Bahcall-Pinsonneault ( 2004 ) solar model if one wants to invoke opacity errors in order to reconcile recent solar heavy abundance determinations with the helioseismological measurement of R _ { CZ } .
We show that the radiative opacity near the base of the convective zone depends sensitively upon the assumed heavy element mass fraction , Z .
The uncertainty in the measured value of Z 
is currently the limiting factor in our ability to calculate the depth of the CZ .
Different state-of-the-art interpolation schemes using the existing OPAL tables yield opacity values that differ by \sim 4 % .
We describe the finer grid spacings that are necessary to interpolate the radiative opacity to \pm 1 % .
Uncertainties due to the equation of state do not significantly affect the calculated depth of the convective zone .