  We analyze the qualitative features in the transition spectra of a model
superconductor with multiple energy gaps, using a simple extension of the
Mattis-Bardeen expression for probes with case I and case II coherence factors.
At temperature T = 0, the far infrared absorption edge is, as expected,
determined by the smallest gap. However, the large thermal background may mask
this edge at finite temperatures and instead the secondary absorption edges
found at Delta_i+Delta_j may become most prominent. At finite T, if certain
interband matrix elements are large, there may also be absorption peaks at the
gap difference frequencies | Delta_i-Delta_j | . We discuss the effect of
sample quality on the measured spectra and the possible relation of these
predictions to the recent infrared absorption measurement on MgB_2.
