A quantitative relationship between auroral brightness and solar EUV produced Pedersen conductance is established by using Lyman-Birge-Hopfield long and short bands of auroral emissions from Polar Ultraviolet Imager (UVI). We used a conductance model characterized by solar zenith angle, solar F10.7 radio flux, and the local magnetic field to estimate solar EUV Pedersen conductance for each pixel of the images. The hourly average IMP 8 solar wind data set is used to derive corresponding solar wind conditions. Pixels of the auroral brightness in Polar UVI images have been binned in terms of magnetic latitude and local time. We relate the auroral brightness to the conductance and find that a positive correlation occurs in the early morning sector, indicating increasing brightness with increasing conductance. An anticorrelation appears in the premidnight region, supporting the previously reported suppression of the discrete aurora occurrence in sunlight. The correlation becomes stronger for the southward interplanetary magnetic field (IMF) condition than for the all B z condition in the early morning and premidnight sectors, indicating that the conductance effect on the auroral brightness becomes significant when the IMF is southward. The afternoon auroral bright spot is not eminent when the ionospheric conductance is low.