cast your eye

cast an/(one's) eye over (something)

To look at something quickly and perfunctorily. I always cast an eye over my desk to make sure I have everything before I leave the office at night. You don't have to read this document in detail—just cast your eye over it when you get a chance.
See also: cast, eye, over
Farlex Dictionary of Idioms.

cast your eye

or

cast your eyes

or

cast an eye

COMMON If you cast your eye, cast your eyes or cast an eye around, over, etc. something, you quickly look at something. Adam cast his eye over his notes again. He cast an eye around the room, at the window that Colin had just smashed. She cast her eye down the list of names. Note: You can also say that you run your eye, run your eyes or run an eye around, over, etc. something. There were various bottles on the shelf above and I ran my eyes over them. Nothing of interest there. He ran a casual eye down the first page of the bank statement.
See also: cast, eye
Collins COBUILD Idioms Dictionary, 3rd ed.
See also:
  • cast an/(one's) eye over (something)
  • cast/run an eye/your eyes over something
  • run an/(one's) eye over (something)
  • run eye over
  • glance over
  • glance over (someone or something)
  • have your eye on somebody/something
  • give (one) the eye
  • give someone the eye
  • give the eye
References in classic literature
If you will cast your eye over this map, you will see that we have at our disposal the whole of the southern portion of Texas and Florida."
Put it to the test and cast your eyes upon the history of mankind.
WE'VE plenty for you to cast your eye over in Home this week.
But cast your eye down the programme that runs until September 13 and some unexpected pop names will leap out at you too.
Now cast your eye over these changing famous faces.
Cast your eye toward Atlanta, where citizens are gearing up - and greening up - for the Centennial Summer Games.
If it's a bit of each-way value you want then cast your eye towards last year's winner Razor Royale.
Of course, there's nothing new about apes loving Beatles music - just cast your eyes to the right