Can a person wear Prescription sunglasses for distance on Shabbos in an area without an ARUV? To protect the eyes from the sun. Without sunglasses its very uncomfortable. It can cause a headache, ect.
The poskim write that in general a person should not wear sunglasses on shabbos outside of an eruv because one is apt to take them off even when outside, such as when going into the shade, or taklking to someone, and since they might be taken off and carry them it is not allowed to be worn outside. In your instance there is some room for leneincy, because you are less likely to take them off outside since you need them for seeing distances. The question in your case would be, what happens during the week when you go outside in the street, do you ever take them off, such as your in the shade, or do you always wear them when outside. If you don’t take them off at all when outside them it would be permitted, according to some poskim, and you have what to rely on, however if you do take them off occasionally outside them then they should not be worn, because you might take them off.
Rema O:CH 301-11, Shmiras Shabbos Khilchoso 18-18, B’tzel Hachochma 4-4-(5), Conversation with R’ Y. Leshinsky shlita.