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". Although the Tenth Doctor then admitted to wearing faux eyewear himself, (TV: Time Crash) this was apparently a lie, as he realised he was slightly long sighted shortly after his regeneration. (PROSE: The Christmas Invasion)

Most incarnations of the Doctor did not employ eyewear of any kind. Those that did actually needed corrective lenses. The First Doctor's glasses, for instance, were of no use to the Second Doctor, who immediately suspended their use after regeneration. (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)

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