Specimen from the National Mineral Collection, photo by Chip Clark. http://geogallery.si.edu/index.php/en/1177807/agate

Iris agates are very finely banded (15-30 bands per millimeter) iridescent agates that I like to call CD agates.  In order to see if an agate has the iris effect, you must bring it home, cut off a thin slice, and hold it up to the light.  The slices also have to be cut perpendicular to the banding to see the rainbows.  The rainbow effect occurs because the thin layers of agate split up the visible light into many beams of different wavelengths, which correspond to different colors.  This is also known as a diffraction grating, and it’s also the reason why CDs have rainbow patterns.

If you would like a technical explanation of how iris agates act as diffraction gratings read this: http://www.minsocam.org/msa/collectors_corner/arc/iris.htm