The intensity of high-order rainbows for normally incident light and c
ertain rotation angles of a cylinder with an elliptical cross section
is greatly amplified with respect to the intensity for a circular cros
s-sectional cylinder. The amplification is due to a number of the inte
rnal reflections occurring past the critical angle for total internal
reflection, and the effect is especially strong for odd-order rainbows
, beginning with the third order. Experimentally, the fourth-and the f
ifth-order rainbows of a nearly elliptical cross-sectional glass rod w
ere observed and analyzed. (C) 1998 Optical Society of America.