This is based on my own experience (having worn glasses for 50 years) and
common sense.

I have had very bad experiences getting accurate eye exams with
ophthalmologists, who are primarily trained to treat eye diseases and
perform eye surgery. Their primary job is not to give eye exams, and they
don't have as much experience at that compared to an optometrist (generally
speaking). Ophthalmologists are MD's trained in medicine, whereas
optometrists are OD's who are focused (no pun intended) on giving eye exams
and dispensing lenses, all day long, every day.

The only exception to my advice might be if you are currently being treated
by an ophthalmologist for an eye disease or recent surgery. Then it might be
advisable for the ophthalmologist to do your eye exam also.

You could legally get a Rx from a brain surgeon to treat your ear infection,
but a general practitioner (or ear, nose specialist) will have more
experience treating you, even if the brain surgeon is much smarter than the
other doctors.