We discuss the effect of atmospheric dispersion on the performance of a mid-infrared adaptive optics assisted instrument on an extremely large telescope (ELT). Dispersion and atmospheric chromaticity is generally considered to be negligible in this wavelength regime. It is shown here, however, that with the much-reduced diffraction limit size on an ELT and the need for diffraction-limited performance, refractivity phenomena should be carefully considered in the design and operation of such an instrument. We include an overview of the theory of refractivity, and the influence of infrared resonances caused by the presence of water vapour and other constituents in the atmosphere. 'Traditional' atmospheric dispersion is likely to cause a loss of Strehl only at the shortest wavelengths (L-band). A more likely source of error is the difference in wavelengths at which the wavefront is sensed and corrected, leading to pointing offsets between wavefront sensor and science instrument that evolve with time over a long exposure. Infrared radiation is also subject to additional turbulence caused by the presence of water vapour in the atmosphere not seen by visible wavefront sensors, whose effect is poorly understood. We make use of information obtained at radio wavelengths to make a first-order estimate of its effect on the performance of a mid-IR ground-based instrument. The calculations in this paper are performed using parameters from two different sites, one 'standard good site' and one 'high and dry site' to illustrate the importance of the choice of site for an ELT.