half an eye

Noun

half an eye (uncountable)

1. A minimal amount of attention.
   • to keep half an eye on something
   • And if the reader can add that throughout the length of the book, during all his immersion in the author's purpose, he still had half an eye for the means whereby that purpose was achieved, no conceivable harm is done.1976, Edward Crankshaw, Joseph Conrad: some aspects of the art of the novel, page 8
2. The slightest ability to recognize or perceive.
   • Thus (as you will see with half an eye, my wise little auditors) these good old dames had fallen into a strange perplexity.1851 June–July (date written), Nathaniel Hawthorne, “The Gorgon’s Head”, in A Wonder-Book for Girls and Boys, Boston, Mass.: Ticknor, Reed, and Fields, published November 1851 (indicated as 1852)...
   • The veil would be torn to pieces in less than a week, or would be made so transparent that any one, "with half an eye,"— as the saying is, though we never recollect meeting any one who only had "half an eye" —would be able to see through it; and if any one did take the veil, it would be because she...1851, “An Interview with the Syrio-Lebanon Family”, in Punch, volume 21, page 154