Somehow I think "Examination of external eye" is ok, with the alternative in consideration being "Examination of an external eye", even though eye is a countable noun in this case. Am I right on this? What kind of rule is that?
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I'm not sure whether or not "external eye" is the phrase that doctors would use (I don't think I've ever heard it) -- but if it is, I think you could say "examination of the external eye."
Why is 'the' necessary or preferred for eye? Is it because it just sounds better? Just saying 'eye' would mean the eye of a person no? Actually just as I'm typing 'eye' I seem to have the tendency to automatically prefix it with 'the' for some reason. 'the eye' rather than 'eye' because of frequency of usage of the former for some reason (eg. because it sounds better?)