  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.
