Answer by Rabbi Chaim Hillel Raskin – Rov in Kfar Chabad Beis, Israel:
One may only walk outside on Shabbos wearing items that are considered either a garment (beged) or an ornament (tachshit), and are therefore nullified to one’s body. Otherwise, it is considered a burden (masui) and one may not carry it on Shabbos even by wearing it.
Moreover, even such items may not be worn outside if they might fall off or they are the type that one may take off and carry in his hand (unless they are attached in a way that he cannot take them off).
One who requires eyeglasses in order to see properly, and therefore wears them all the time, is allowed to walk outside with them, for they are considered as a garment and not an additional item.
While poskim in previous times were concerned that one’s glasses might fall and one will come to carry them, contemporary poskim write that that this concern is no longer applicable to most current glasses.
Reading glasses, however, are not needed for walking and they are therefore considered something extra at that time. In addition, there is a concern that he might take them off or slide them back over his head. Bifocals may be worn if one wears them all the time.
One who is just starting to wear contact lenses should not go outside with them on Shabbos if there is concern that he might remove them because they irritate his eyes.
Regular sunglasses that are for protection from the sun may not be worn outside, even in a situation where they help him walk, because he may take them off when he reaches a shady area and mistakenly carry them. The same is true for clip-on shades.
However, prescription sunglasses are permitted if he won’t take them off even in a shady area because he needs them to see.
Certainly, prescription glasses that change color in the sun are allowed since they are like regular glasses in the shade. (It isn’t an issue of coloring on Shabbos since the color change is temporary and will disappear soon after.)
For one who must wear sunglasses all day due to a medical concern, the sunglasses are considered his regular glasses, and he may wear them outdoors on Shabbos as well.
Published in the Weekly Farbrengen, a publication of Merkaz Anash. See Sources