An ophthalmologist is a medical doctor who looks after eyes: checking sight, treating disease, and often doing eye surgery. The ending -ist points to a person, not to the subject. The subject itself is ophthalmology — that is the study. In English-speaking clinics people also meet optometrists, who test sight and prescribe glasses, and opticians, who make and sell the glasses. Those are different jobs, though students (and even adults) often fold all three into one idea of 眼科. In Taiwan the everyday hook is 眼科醫師. This is a long, formal word; even native speakers trip on saying it. Though actually, if a line ever tells you this word “means the study of the eyes,” that line has slipped: the study is ophthalmology; this word is the doctor.