Brainy specs

The Fifth Doctor wears his pretend eyewear. (TV: Frontios)

The term "brainy specs" was invented by the Tenth Doctor to describe glasses that the Fifth Doctor didn't "even need" but which made him "look a bit clever". The Tenth Doctor then admitted to wearing faux eyewear himself, (TV: Time Crash) although another account implied that this was a lie, as he had realised he was slightly long sighted shortly after his regeneration. (PROSE: The Christmas Invasion)

At any rate, the Curator later stated that he too owned glasses that he would occasionally put on to make himself look clever. (PROSE: The Day of the Doctor)

Most incarnations of the Doctor did not employ eyewear of any kind. Those that did actually needed corrective lenses. For example, the First Doctor's glasses were of no use to the Second Doctor following his regeneration; when he put the glasses on out of habit to look at the Earth Examiner's badge, everything went blurry and the Doctor soon realised he didn't need his glasses any more. (PROSE: The Power of the Daleks)

Likewise, the Eleventh Doctor appropriated Amy Pond's reading glasses and noted that they did, in fact, make reading easier. (TV: The Angels Take Manhattan) Indeed, Amy's glasses were the only glasses ever carried by the Doctor which were definitively known to have resulted from an optometrist's prescription. (TV: The Power of Three)

Looking back, however, the Curator lumped the Eleventh Doctor's glasses in with the Tenth's as spectacles worn mostly to make himself look clever. The Curator, who occasionally employed the same technique, thought that "it worked". (PROSE: The Day of the Doctor)