H.G. Wells' The Invisible Man (the original) dealt with it.
The eponymous character tests his formula on a cat first, and the author notes 'there remained two little ghosts of her eyes'.
I seem to recall from somewhere that he injects his eyeballs with something to achieve the effect.
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In the Recluce universe, LE Modesitt Jr deals with this.
his "Order Mages" can bend light to become invisible.
When they do, they are also blinded because they can not see.
EDIT
I have also remembered the TV show Invisible Man (aka I-Man) dealt with this as well.
the "I-Man", when invisible, could not see in the "normal" spectrum of light.
In the show, they hypothesized that he "saw" in the infra-red spectrum.
They often leveraged this "fact" in the show.
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In Warren Ellis's Planetary he specifically addresses this with his version of the Invisible Woman from the Fantastic Four.
She needs special goggles to see -- otherwise she's blind while invisible.
A variant can be found in James Alan Gardner 's books Expendable and Ascending .
One of the characters, Oar, is translucent to humans.
However, it's made clear that this was only applicable in the wavelengths of normal human eyesight, and she's not completely invisible.
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Well, there is one kind of invisibility that alleviates the problem.
If you don't bend the light but absorb it and create it anew on the other side of the body you want to conceal, then you can do whatever you want inside, including displaying the outside world.
This is nicely implemented in Ghost in the Shell.
You'd still need some way to record the light hitting you but
that's plausible with something like distributed light field technology that could in principle use a large number of microscopic, lens-free sensors.
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This is actually the punch line of a short story (I guess by Robert Sheckley, but may also be Arthur C. Clarke's 'Tales From The White Hart').
It evolves at a bar where a guest confesses to another that he once helped an alien of a race that is known for its generosity with a paperclip and is granted a wish.
He asks for being invisible once a day for an hour and is persuaded by the other guest to stay on until it happens.
He stays put at bar stool eventually becoming both invisible and blind.
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One problem I've always thought of with science fiction characters becoming invisible is that they should go blind, because their retina does not catch any light.  Obviously a lot of soft SF or fantasy would gloss over this. But I'm sure that hard SF authors have had a go at it. How can invisibility and sight be reconciled?
Invisibility should cause blindness: how does hard sf cope?
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H.G. Wells'  The Invisible Man  (the original) dealt with this issue, as did LE Modesitt Jr in the Recluce universe. This is addressed specifically in Warren Ellis's  Planetary, with his version of the Invisible Woman from the Fantastic Four. A number of works, including The Invisible Man, Recluce Universe and Planetary deal with the issue of invisibility and blindness. Moreover, there is, apparently, one kind of invisibility that alleviates the problem of blindness.
The Invisible Man, Recluce Universe and Planetary all deal with the issue of invisibility and bindness. There is apparently one kind of invisibility that alleviates the problem of blindness.