Previously the effect of atmospheric dispersion on telescope performance has attracted only relatively little attention. This may be due to the fact that the dispersion effects have been evaluated in relation to the size of the diffraction limited resolution angle of current telescopes, or to seeing limited telescopes. However, since the resolution angle is inversely proportional to telescope diameter, dispersion and dispersion compensation becomes increasingly important for extremely large telescopes (ELTs). In this paper we present a simple model for the dispersion effects in telescopes with adaptive optics (AO). The model addresses the expected loss in Strehl ratio when the atmospheric wavefront error is measured at a wavelength different from the wavelength of observation. Also, the bandwidth over which the correction will be of a given quality is evaluated. Related to AO performance, the consequence of using laser guide stars (LGSs) for probing the atmosphere may be that the measured wavefront error must be rescaled to the wavelength of observation. This places special demands on the AO control loop. Since linear atmospheric dispersion compensation need not cover a larger bandwidth than the AO compensation, an atmospheric dispersion compensator (ADC) can be designed for narrow band operation. As an example of the benefits to be obtained from this, we briefly present the proposed ADC for the Euro50.