Achieving diffraction limited imaging with future ground-based optical telescopes will require adaptive optics for correction of atmospheric turbulence and also efficient techniques for atmospheric dispersion compensation. We study the benefit of using a linear atmospheric dispersion corrector (ADC) coupled with a deformable mirror on a 42-m Extremely Large Telescope (ELT) operating in the VIRJ spectral bands. The ADC design consists of two identical thin wedges made of F5 glass. The amount of dispersion introduced by the ADC is adjusted by translating one of the wedges along the optical axis so that it always cancels atmospheric dispersion as it varies with telescope elevation. We show that the ADC working in conjunction with a deformable mirror provides diffraction-limited image quality over a 1-arcmin field.