When we say "cast an eye", it implies a quick glance or a brief look. There are other terms that can be used interchangeably with this phrase. For instance, we can replace "cast an eye" with "glance", "glimpse", "peek", or "look quickly". Each of these synonyms is suitable for a situation where we want to express the act of looking briefly at something. We could use "cast a glance" or "take a quick peek" to express that we are doing something with a sense of urgency or secrecy. Nevertheless, all of these synonyms mean the same and can be used interchangeably in most situations.