We present diagrams that show how layers in atmospheric thermal struct
ure are related to the altitudes at which they are seen tangentially.
These dip diagrams show that the inferior mirage greatly magnifies the
apparent angular size of the lowest few centimeters of atmosphere. Co
nversely, inversion layers below eye level are compressed-even to zero
apparent thickness, in ducts. The diagrams show that, even when dista
nt objects are miraged, the ray crossings occur beyond the lowest poin
t on each ray where the line of sight is tangent to a horizontal surfa
ce in the atmosphere. Therefore the apparent altitudes of these tangen
t points are a monotonic function of their actual heights in the atmos
phere. This monotonicity explains an apparent paradox in low-Sun image
s. (C) 1998 Optical Society of America.