The idiom "burn the midnight oil" means to work late into the night, often with great diligence and effort. This phrase dates back to a time when oil lamps were the primary source of artificial light. To "burn the midnight oil" literally meant to keep a lamp lit and continue working or studying long after sunset, consuming the oil in the lamp throughout the night.
Today, the idiom is used metaphorically to describe anyone who stays up very late to complete tasks, study for exams, or work on projects. It implies a strong commitment and a willingness to sacrifice sleep to achieve a goal. For example, a student might "burn the midnight oil" before a major exam, or an employee might do so to meet a tight deadline. It emphasizes dedication and hard work, often under pressure.
The alternative options are clearly incorrect: "sleep early" is the opposite of the idiom's meaning, "light a lamp" describes a literal action but not the figurative meaning of working late, and "waste time" contradicts the diligent effort implied. Thus, "work late" is the precise and correct interpretation of "burn the midnight oil," signifying extended periods of nocturnal labor or study.