In chapter 10 in brave new world what is Barnards punishment?
In the dystopian society created by Huxley in "A Brave New World", the most cherished quality is acceptance and approval. Babies are all born in labs, "Family" is a thing of the past, free love and universal access is what society is all about in the Central London area.
Bernard is an Alpha, the elite class, but he suffers from slight differences that cause him to be a bit of an outcast. His hopes for acceptance seem to be coming true when he finds John Savage on an outing. He brings him back, a savage in reality by their standards, and parades him before all of his contemporaries as an oddity - until John tires and refuses to participate any more. Trouble stirs and that is not allowed.
Now, as to your question, Bernard is exiled to Iceland as punishment for his threat to the order of the usually calm and controlled society. This would serve as a very real punishment for him, since all of this was precipitated by his desire to fit in and to be included, not excluded.