Several molecules important in the chemistry of the stratosphere, including N2O, H2O, HNO3, and several chlorofluorocarbons, photodissociate in the wavelength interval 1750-2050 Angstrom. The transmission of solar radiation in this spectral region is largely controlled by the Schumann-Runge (S-R) bands of molecular oxygen. The absorption cross sections of oxygen in this region vary by several orders of magnitude as a function of wavelength, resulting in large variations in the magnitude of solar radiation penetrating into the middle atmosphere. It is thus of interest to examine the potential effects that a knowledge of the fine structure of the solar spectrum would have on the accurate calculation of stratospheric photodissociation rates. A U.S. Naval Research Laboratory solar spectrum with a resolution of 0.07 Angstrom has been used to compute high resolution photodissociation rates for several molecular species. Computations have also been performed in which this solar spectrum has been degraded by roughly a factor of 100. These calculations show that knowledge of the fine structure in the S-R region of the solar spectrum produces only a marginal (1-2%) improvement in the computation of the photodissociation rates. This results from the fact that the photodissociation rate is a spectrally integrated quantity, and that there is, on average over the S-R bands, no correlation between the solar spectrum and the oxygen absorption cross sections. This very small improvement should be compared with the much larger uncertainties in important chemical reaction rates, absorption cross sections, and quantum yields, which are often 50-100%.