Why does “iris” mean the coloured part of the eye in English?

The answer to this question draws on the Greek word ιρις, iris, which means (in Greek) rainbow. I am interested in why English uses that same word for the coloured part of the eye.

a flat, coloured, ring-shaped membrane behind the cornea of the eye, with an adjustable circular opening (pupil) in the centre.

Google Dictionary

The coloured area of the eye is, of course, a full circle.

So why does ‘rainbow’ (a half-circle) in Greek - transfer to 'iris' (a full circle) in English?

A rainbow is only seen as a full circle from above -

Full circle rainbow was captured over Cottesloe Beach near Perth, Australia in 2013 by Colin Leonhardt of Birdseye View Photography. He was in a helicopter flying between a setting sun and a downpour.

This has implications regarding the original quotation in the previous question – the matter of the covenant and the concept of ‘seeing’ through the covenant.

I'm a very devoted fan of both rainbows and beautiful eyes. And that is relevant to the question, because:

I'm sure many people would agree that rainbows and beautiful eyes are equally fascinating. Both phenomena captivate one's attention in the awesome way that they manipulate light and color. And they are equally divine.

I know a dear lady named Iris, too. She and her wonderful husband, Jose, have an adorable son. I doubt there is any sweeter family in the world. They're Puerto Rican, and according to Google Translate, Iris is Spanish for:

Diaphragm muscle, opaque and contractile, located in front of the lens of the eye and in whose center is the pupil.

But I'm not fluent in Spanish, so I wouldn't mind hearing more about it from someone who is.

According to Etymonline:

iris (n.) late 14c. as the name of a flowering plant (Iris germanica); early 15c. in reference to the eye membrane, from Latin iris (plural irides) "iris of the eye; iris plant; rainbow," from Greek iris (genitive iridos) "a rainbow;" also "iris plant" and "iris of the eye," a word of uncertain origin, traditionally derived from PIE root *wei- "to bend, turn, twist."

Iris was the name of the minister and messenger of the Olympian gods (especially of Hera), visibly represented by the rainbow (which was regarded as the descent of a celestial messenger). From the oldest parts of the Iliad the word is used of both the messenger and the rainbow.

The eye region was so called (early 15c. in English) for being the part that gives color to the eye; the Greek word was used of any brightly colored circle, "as that round the eyes of a peacock's tail" [Liddell & Scott]. Another sense in Middle English was "prismatic rock crystal." Related: Iridian; iridine.

In conclusion, my Webster's dictionary lists both Latin iris and Greek iris for the root, along with the Latin meaning of iridescent stone and the suggestion to see the definition for iridescent, which is from the same root.

Iridescent ~ having or showing an interplay of colors like the rainbow; prismatic.
Iridian ~ pertaining to the iris of the eye.
Iridic ~ relating to the iris of the eye.

All adjectives, from Webster's New 20th C. Dictionary, Unabridged, 2nd Ed.

The first OED citation for the anatomical (meaning ocular, not botanical) sense for iris seems to tell the tale when it deliberately connects it to the rainbow:

1525 Anothomia in tr. H. von Brunschwig Noble Experyence Handy Warke Surg. sig. Bjᵛ/2
There be iij. materyall circles yᵗ ronne about the iye, and because they be so different of colours they be callyd yrides or rain bowys.

That uses the classical plural for iris: irides, as in iridescent.

Eye-color can be hard to pin down. Sometimes it seems more sensible to call it a rainbow. :)

^{_{Image credit: my own}}

Etymonline explains that the Greek word iris also referred to any bright colored circle, and from that the part of the eye:

The eye region was so called (early 15c. in English) for being the part that gives color to the eye; the Greek word was used of any brightly colored circle, "as that round the eyes of a peacock's tail" [Liddell & Scott].Another sense in Middle English was "prismatic rock crystal."

From world-bird-sanctuary.blogspot.it

Note that the term is used also in there languages such as French and Spanish iris and Italian iride.