Is farewell appropriate when saying goodbye to a teacher?

You can use either, but *farewell* is technically the more appropriate and polite one for when you don’t ever expect to meet again. It’s much less common than *goodbye* in normal contemporary use. Your teacher will probably be pleased and touched if you go old school on this; I certainly would.

Some people make a very pedantic distinction between the two, but the vast majority of people understand them to be interchangeable. Yes, it's appropriate.

Goodbye is much more casual. Use farewell if you were fond of the teacher and wish to be a touch more sweet with your partings.

Native speaker from the USA and English teacher here (with an actual diploma in English as well). Real answer below. No, not really. It’s not really appropriate in any context, it sounds archaic and artificial in pretty much any modern context I can think of. That said, speak however you damn well please, twist the language as you wish, screw the rules. But you deserve to know (if you care) that a lot of people might think you sound a little funny if you do that.

Farewell has fallen out of common usage because it arose mainly because people would have to walk or ride a horse for miles to get to where they were going which could take days or weeks. It basically means the same as "safe travels." To fare in this sense means "to journey." Because of this it might seem odd to a native speaker. It might be appropriate still if the person is going on a long journey that will take days or weeks (which can still happen it's just rare). Goodbye had a similar origin but it has become accepted for general usage. Goodbye started off as "god be with ye" also wishing someone a safe journey.

It's a formal, literary word. You should use something more common, such as "goodbye."

Farewell is very formal. It's excessively formal in the vast majority of cases and is hardly ever used unless someone is intentionally trying to sound dramatic. Goodbye is the standard.

Say fare thee well

I would say, I am going to miss you. Your class was enjoyable and you are a real pro!

I don't think I have ever seriously said "farewell" to someone in my life. It's quite dramatic and old-fashioned. Just say goodbye and thank your teacher for their work with you (assuming you appreciated the classes!)

Nobody has said "farewell" to their teacher--or anyone else-- since The Sound of Music. That's like saying "greetings and salutations" when you first meet someone.

It depends on the tone and context although it is rarely used. If you want your message to sound respectful and heartfelt then you can use it. For example when you are graduating or your teacher is retiring or relocating. "Farewell, dear teacher. As I graduate, I just want to say thank you for your endless support, courage and dedication." In many cases more usual and casual alternatives are: Goodbye or See you tomorrow.

Can't go wrong with Shakespeare. "If we do meet again, why we shall smile; If not, why then this parting was well made."

I’ve honestly never used the word farewell; it’s very archaic. There’s never going to be a time when it’s appropriate to use it because it’s not in use.

Dramatic like i would wonder if i would ever see that student again. Its an old word and sounds like it. I’ve only ever heard it in meoldramatic movies or when people are being funny.

I don't think I've ever actually heard someone use the word farewell. People don't really say that, at least not in America. Technically it would be the correct time to say it, so you could if you wanted to.

Better than either one would be to express your thanks and appreciation.

So I use the word farewell often. Its my thing. It is not a common word, though. You might get funny looks. Usually its just "seeya later"

I think farewell is appropriate to use, since it might be the last time you the person. It’s not that other commenters are wrong about it, but I think they are overstating how much more formal or archaic it is to say.

Farewell to my ear feels dramatic or theatrical. Your meaning will be clear but no one really uses this word. Goodbye is perfectly fine.

Yes. Fine.

I’d say Goodbye but I’d add something onto it like “I really enjoyed our english classes”to express your gratitude (It feels more natural to say this in my opinion). Farewell isn’t really a term used (or at least i use) anymore. There isn’t a difference between farewell and goodbye. Farewell just comes from middle english meaning “travel safe”. It’s used to be poetic or formal. Goodbye is just more used in modern contexts.

Almost nobody uses farewell in everyday speech anymore unless they’re being funny.