眼科
がんか · ganka · JLPT N1 · noun
ophthalmology
👁️ 眼 (eye) + 科 (department/subject) = the medical department of the eye
眼科 is built from 眼 'eye' and 科 'branch of study or department', so it names the field that studies and treats eye disorders. Ganka sounds like 'gan-ka': 'gan' like 'gun' is a hint to 'eye' only if paired with the kanji.
眼 — eye radical 目 + 艮 (phonetic)
眼 is a semantic-phonetic compound. The left side 目 means 'eye' and gives the meaning, while 艮 on the right supplies the sound. Originally referring to the eyeball, it broadened over time to mean 'eye' generally and, by extension, 'a hole' or 'key point'.
科 — grain 禾 + measure 斗
科 combines 禾 (grain) and 斗 (a dipper/measure), originally depicting the act of measuring or grading grain. From this, it extended to mean classification, category, and branch of study. Today it commonly appears in words for science (科学) and academic disciplines.