I love reading user studies like this recent one from Nielsen Norman Group, where they talk about the user experience for using the magnifying glass icon for search.
All in all, they say it works quite well. Users tend to recognize the search icon even moreso than the “hamburger” icon that’s prevalent today, which they recommend using a label for. Displaying a label alongside the hamburger icon is also supported by Exis Web (a border makes it even better, interestingly).
The Nielsen Norman Group also gives some good practical tips for better search engagement strategies that make it well worth the read.