For many types of PPE (e.g. eye protection, ear protection), OSHA further refines their rules specifically for that type of protection. For example, according to OSHA, the requirement for Eye and Face Protection is as follows:
OSHA Title 29 CFR Part 1910.133 Eye and Face Protection The employer shall ensure that each affected employee uses appropriate eye or face protection when exposed to eye or face hazards from flying particles, molten metal, liquid chemicals, acids or caustic liquids, chemical gases or vapors, or potentially injurious light radiation.
Further Resources
OSHA's regulations on PPE can be found in Title 29, Code of Federal Regulations 1910 Subpart I
The ANSI standard that cover general PPE is ANSI/NFPA 70E -- Personal Protective Equipment.