The Occupational Safety and Health Administration (OSHA) sets in place rules and guidelines that focus on protecting workers in the workplace. One of the requirements specifies that workers should have appropriate eyewear when eye-related injuries are most likely to happen.
As we mentioned above, when working with hazardous elements it is important to protect your eyes with safety glasses. The particular regulation OSHA 1910.133 means that safety glasses need to be tested and approved for the workplace by meeting certain standards.
So in short, yes, safety glasses should be approved by OSHA regulations. It is important that the glasses in question clearly state whether they are OSHA-approved or not. You may also find that standard protective eyewear has an ANSI rating. The latter assures that the safety glasses meet impact resistance and visual clarity requirements.