Phrasal verbs as hyphenated adjectives

Question

So I recently had a question of how to translate a seemingly simple phrase which gave rise to a really puzzling dilemma. The phrase itself was "the eye which had been operated on", it was passive. However, the original language only used one single adjective + "eye", and I wanted to somehow retain that so as to not make the translation too wordy.
One option was to simply say "the treated eye", which was OK. But I also wondered whether I could use "operate" as an adjective. Which led me to 2 options: "the operated eye" and "the operated-on eye". The latter seemed to be more suitable because we normally say that surgeons "operate on" an organ/limb/tumor/... and people have operations "on" parts of their bodies, so I ought to keep the preposition. The former sounded a little ambiguous, since "operate" could be confused with "manipulated, controlled" as in a "machine which is operated from a control panel".
My question is twofold, I guess. Am I correct in thinking that phrasal verbs may be used as hyphenated phrasal adjectives and, if so, is doing so appropriate in this particular case?

fev · Accepted Answer

The best way of saying the eye which had been operated on is by omitting "which had been":

the eye operated on

Operated on would be a reduced passive relative clause:

the "reduced object passive relative clause" is a type of nonfinite clause headed by a past participle, such as the clause found here in:

The animals [who are] found here can be dangerous. (Wikipedia)

The particularity of this structure, is that the passive clause consists of a verb followed by what CAGEL calls a specified preposition.1 This is a prepositional passive:

In the prepositional passive construction the preposition remains next to the verb. Passives are much more widely available
with specified prepositions, but they are not admissible in all cases. Compare:

*Some old letters were come across 
Her book was referred to.

(p. 276)
there are cases when we can speak of

the formation of deverbal adjectives from passive
V+P sequences:

our effective, relied-upon marketing strategy
a first novel from an as yet unheard-of author

So you might argue that your suggestion, the operated-on eye, stands in this category.
But you must be aware that:

Not all prepositional passives can be used to derive prenominal adjectives:
a. *a sailed-under bridge, *a sat-beside grouch
b. *a put-up-with situation, *a made-up-for loss (article)

I would call "operated-on" non-standard, and would recommend the other word order I suggested in the beginning: The eye operated on. When I looked up "the operated-on patient", I found very few results (not even 20k) spelled without the hyphen:
e.g.

Laparoscopy per se improves the patient outcome allowing low pain, reduction of pulmonary dysfunction or less fatigue, better mood and psychological status on the operated on patient. (medical site)

GNgram finds no instance of "operated-on eye":

1 Verbs that require a specified (one particular) preposition are expressions that are either (1 ) figurative —the verb is literal but the preposition is metaphorical— or (2) idiomatic— neither verb nor preposition keeps its original meaning; they are paired together to form a particular a meaning. Olivia ran into trouble. (fig. "inside a situation")// Olivia ran into a friend. (idiom "met by chance"). (Grammarquizzes)

Greybeard · Answer

Informally/colloquially, you will find some past participle of phrasal verbs (verb + adverb) used as adjectives in the way you describe. However, you must be careful in accurately identifying a phrasal verb rather than {verb + collocated preposition}:
Intransitive verbs cannot be used this way:
The species died out. / *The died-out species used to live in Africa. [wrong] / The extinct species used to live in Africa.[correct]
Words such as “in, up, through, over, etc. etc” can be adverbs or prepositions. The formation of compound adjectives does not work if the word is a preposition rather than an adverb:
John was put upon (adv.) by David, and eventually the put-upon David rebelled. (correct)
The vase was put upon (prep.) the table by John / *The put-upon vase looked expensive. [wrong]
This is guidance rather than a rule: some phrasal verbs work; some do not work; some sound strange, and some can be imaginatively descriptive.
Phrasal verbs usually have a closely synonymous single word transitive verb. The single word verb should be your first choice of adjective.

One option was to simply say "the treated eye", which was OK. But I also wondered whether I could use "operate" as an adjective. Which led me to 2 options: "the operated eye".

To operate (in this sense) is intransitive and thus “[up]on” is a preposition – thus it does not work as a compound adjective. (I repeat: you may hear this use informally, or colloquially.)
In your case “treated” is accurate, idiomatic, and correct.

DjinTonic · Answer

operate
II TRANSITIVE SENSES
8. Surg. To operate on.
1908 I know of two cases of pyelitis that were operated in mistake
for appendicitis.
...
1930 Of those questioned 26 1/2 per cent of those question used
'operated him', 40 per cent used 'operated on', and 33 1/2 per cent
used 'operated upon him'.
[From the OED]

Adjectival use, as in the operated eye, abounds in the medical literature, for example:

Under room lighting, patients could simultaneously use prosthetic
central vision and the remaining peripheral vision in the operated
eye and in the fellow eye. Medical journal paper 2021

Patients with proximal femoral fracture (PFF) often develop
postoperative edema in the operated limb. Medical journal article (2007)

Medical professionals assume a layperson will take this construction in stride, as in these patient instructions:

During the first week
Avoid getting soap in your eye. Avoid creams
lotions and make-up around the operated eye. (2020) [no pun intended]

A Johns Hopkins webpage has:

What should I expect after glaucoma surgery?
Blurry vision in the operated eye is common during the immediate recovery period.

Phrasal verbs as hyphenated adjectives

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