The image quality of a fluid atmospheric dispersion corrector (FADC) is analysed and presented. The FADC is located at Cassegrain focus to correct the atmospheric dispersion passively at Australian astronomical telescope. It is shown that an FADC with diameter 10mm can correct the atmospheric dispersion over a field diameter of 20" in the spectral range between 0.4μm to 1μm, and to zenith distance of 52°. The FADC image quality is well controlled within 0.27" for the telescope operation range. The residual atmospheric dispersion is 0.1" for on axis field and 0.20" at the extreme field (10") at zenith distance of 52°. The FADC-induced shift in the centroids of the images is less than 10μm (0.067"). The FADC can work up to the field of 5' at Cassegrain focus and its image quality is similar to its on axis performance. Our on-sky demonstration results agree well with our simulations.