青 ao seems to be used very much interchangeably for both blue and green. Why is that so, and how does 緑 midori play into this?
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Beside some of the historical examples mentioned by Derek, there is also an inherent nuance that separates 青 from 'blue', as it is commonly understood in Western culture (and similarly, albeit less strongly, for 緑 and 'green'). This is not unique to Japanese-English and probably applicable to any pairs of sufficiently separate cultures: colours are, for a large part, an artificial construct and there is only limited reasons two people should pick the same arbitrary frontier along the green-blue continuum (or red-orange, or yellow-green etc). I recommend digging in Google Scholar for more on that, but it's worth mentioning that there is much debate on what the causes and extent of these differences between cultures are.
Anyway, back to 青/緑: leaving aside the fact that the past 100 years of intermingling with Western culture have no doubt influenced the native Japanese perception of these colours, there is still a real difference between the range of what a Japanese will call 青い and a Westerner call 'blue' (talking about pure colours here, not objects' traditional colours, which might be tied to historical reasons). 'Blue' for 青 and 'green' for 緑 are just approximations (as are probably most other native colour translations).
A diagram might be the easiest way to put it. Assuming that horizontal line represents the true continuum of hues from blue to green, and the vertical bars, the separation between the two colours in Japanese and English respectively, you'd have:
As a result, when talking about something on the far left (say, the sky) or the far right (say, fresh verdure), both English and Japanese words agree quite well. If you pick things that are in that middle area where the definitions do not match, you get these quizzical looks and people arguing "what do you mean green? it's obviously blue!" etc.
Sorry for the longwinded answer to what is a fairly basic/obvious point... ;-)
This page in the 日本語Q&A over at ALC addresses this question. Apparently the historical definition of 青【あお】, even when defined narrowly, covered an entire range of colors which are today separated as 青【あお】, 緑【みどり】, and 藍【あい】 (indigo). This trend carried into the modern language, and many words which refer to things that are actually 緑【みどり】 still use 青【あお】: 青葉【あおば】 and 青竹【あおだけ】 are two examples given on the linked page. (This in spite of the fact that 緑【みどり】 has existed alongside 青【あお】 all this time.)
Apparently when traffic signals came along, 緑信号【みどりしんごう】 was the official name at first, but it was eventually overtaken by 青信号【あおしんごう】 in common use and this latter name became the official term.
This partially also has to do with the fact that in old Japanese they only used four colours: あか・あお・しろ・くろ. Obviously, with this limitation, あお came to represent a wide range of different cool shades. Then once more "colours started to be used", a lot of things retained their original descriptions as あお.
Edit: Here is that handout I have from my Japanese teacher which I describe below in the comment. It is from a book she has, but I don't have the reference for it.