NEVER MIND

It would generally be a good idea for a student not to say anything, unless the teacher brings it up. Slip into your seat and keep your mouth shut. If the teacher comments, then apologize--say i'm sorry and leave it at that. Teachers don't necessarily owe the students an apology. There is a claim by some university students to the effect that you don't have to wait around for a teaching assistant (a graduate student) and you can just leave (i don't think that's a good idea); but that a professor, someone who has a doctorate, has fifteen minutes of grace. They can be fifteen minutes late, and you have to wait for them--they owe you no apology.

These are cultural questions. Americans rarely apologize to anyone unless they have clearly blundered. Canadians apologize to everyone, all the time. If a Canadian is not paying attention, and walks into a lamp post, he will apologize to the lamp post. You will know your own culture better than anyone here does, you are best qualified to know how to handle this situation. There are no universal etiquette rules.

Set: Americans rarely apologize to anyone unless they have clearly blundered.

////////

Even when the USA has clearly blundered, committed heinous war crimes, egregious acts of terrorism, shot down civilian airliners, ... they don't and won't apologize. Naziism repeated over 250 years!

Thank you~

I also think culture is very important. In China, the students apologize because the tradition, they must respect their teachers; but for teachers, they apologize because they are asked to do that. Anyway, everyone can be late, so it's OK if students or teachers say 'never mind'.