Well, aren't you a lot of fun. If we can assume it is possible for people to become invisible, then we can assume it is possible for them to see while invisible too. Maybe the light doesn't pass through you, maybe it just wraps around you somehow, in that case, I guess the eyes could still work, assuming a little bit of light passes through your pupil.
If I'm wrong and that wouldn't work, then let's just pretend a wizard did it and give a real answer.
Or we could assume that one has a suit which has the ability to instantly receive and transmit a picture via lots of tiny cameras therefore it would be possible for you to see AND be invisible whilst satisfying the laws of physics
I'd go into the zoo and free all the animals ;D that and throw poo and other awkward substances at people to laugh at their reactions ;D
Ooh... Well, I would first leave a note for my parents and leave before they wake up, so as to not have them think I was kidnapped, then I would walk over to the convenience store and take some candy. I would go to multiple convenience stores, always taking a small amount of candy, maybe one chocolate bar, so as to not arouse suspicion. *This is assuming that my clothes are invisible, and anything in my pocket is too.* I would then walk over to my friend(s)'s house and torture him methodically. If they are sleeping in, I would kick their... unmentionables... and when getting dressed I would rip the clothes out of their hands. It is now 10:00 AM I head downtown. I go into a museum, find a suitably dark room, and make scary noises and occasionally grab people's arms. I then head to the boat museum and make the oars in the rowboats row, seemingly by themselves. I'd find a good pizza place, sneak into the kitchen and take one piece. I'd go into a movie theater and watch a movie, possibly taking popcorn from the people next to me. It is now 2:00 PM I'd probably paint something rude on a major road after blocking it of with something. I would then proceed to go to the Legislature building and yell while the politicians are debating something.
I'm getting bored and my post is too long so I'll stop here.
To quote TVtropes on the problems of invisibility:
Invisibility - Applies not just to you, but to things you are carrying, or wearing. Any dirt on you becomes invisible, and either you get clothes made of some suitable material, or provide some Fan Service. Also, your light distortion fits that of your surroundings, and food remains invisible through the digestive process.
Also also, to use an eye normally one must at least have a lens bending the light (thus being visible at least as glass-like objects), pigments in sensitive cells absorbing the light (as opposed to passing right through just like, say, x-rays) and something preventing the retina from blanket exposure by light not focused with the lens, that is, blocking all the rays not coming in via the pupil, including those from behind the retina. Oh, wait, doesn't that add up to almost a complete eyeball?
All of which really raises the question, what counts as an invisible person's body? Just his own cells with his own DNA? Then what about the bacterial colonies in the intestinal tract? What about the mitochondria in each cell, which have their own DNA? What about the lifeless liquids such as stomach acid and fluid in the eyes? What about dead cells, like hair and fingernails? Or the entire outer layers of skin, for that matter?
Some Invisible characters can extend the light-warping field over whatever they touch, eliminating some problems but adding othersâ" conscious selectivity is required, otherwise if they bump into something, that item might blink in and out of sight, making them fairly easy to track, especially crossing a crowded room. The issue of how large an object their field can cover also comes up in many continuities. Invisible Streaker is usually the result of lacking these Required Secondary Powers. A standard aversion of these required secondary powers is psychic invisibility, which is a mental or hypnotic effect that causes everybody to ignore you. The upside is that this automatically also foils hearing and smell; the downside is that it tends not to work on cameras.
You could be filmed, sure, but if it's a mere mortal manning the security cameras (or watching them later for whatever reason), your power may extend through the camera to the viewer as well. So again, you're there, but no one sees you. Depends on the inner mechanics of the power. Some story exacerbates this power to the point of forcing people to retcon their perception to ignore the psychically invisible character. For example, if he takes your sandwich, you change your memory so that you never had it, and possibly wonder why you bought a Coke but not a sandwich, considering you are hungry. Of course, that does not keep you from triggering the laser tripwire that fills the room with toxic gas or anything else that is automated, unless the automation takes the form of a sentient AI.
Michio Kaku of Scifi Science proposed the best practical path to invisibility is a form-fitting suit that bends surrounding light. This suit has small eyeholes which doesn't have this light-bending attribute, allowing the user to see. His eyes would still be somewhat visible, though they may not be that noticeable, depending on the environment.
So, if it was a suit that bent around me and still allowed me to see and stuff, I'd probably just follow some random person home and spend the day hiding in their house xD
