Aside from just bending the light around a subject, bending light along other paths is also useful.

1) Bend light from one place to another to cover over something. This is sort of like the clone stamp in photo-shop or paint.net.

Example: An invisible person standing in the grass, dirt, or water displaces the surface with a dent in the shape of their footprint. To correct defects in the illusion one might bend light from a nearby patch of ground to cover over the part of the image where the feet were.

2) Bend light to make something look like its in a different location.

Example: Someone is in a fight with you. You bend the light a little to the left, so everything looks shifted over. Now every time they aim at you they miss badly.

Example: You are afraid of snipers. You routinely bend your image so that an ordinary person could never get a good shot.

This is accomplished by bending the light in a vortex or swirl pattern. In the figure below you are at A. Light images W, X, Y, Z come out from A at different angles. You bend them all slightly clockwise. Now observers O1, O2, O3, O4 (instead of seeing your true image at A) see images I1, I2, I3, I4 instead. To each observer you will appear to be in a slightly different position, but none of them will see your true position.

Of course since you are smoothly swirling the light you are really generating an infinite number of illusions, each at slightly different angles. The great thing about this trick is you don't have to know where the observer is for it to work, and it works for infinitely many observers. Each trick has its weaknesses and the catch with this one is that someone directly overhead would still see where you were (although you may appear rotated).

3) Bend only some of the light. Now you have two images.

Example: You are walking down the street alone. You bend the image of yourself partly so that from certain vantage points it looks like there is two people.

The figure below shows how this is done. You are at A. Light images X and Y are exiting you from different angles. Ordinarily observer B sees image X but does not see Y because it is going off a different way. You take the light going through cross section P and bend it so that it is directed at B. Now B sees Y and it looks like there is a copy of you at C.

Of course one limitation is that you must know where B is in order to direct the duplicate image at them. Also an observer at D will just see you as a black hole since you stole their image of you. To avoid this, just take light from an angle that misses all the observers.

Of course you can extend this to make even more images of yourself (or anything else for that matter). In the figure below, you are at A. Light images V, W, X, Y, Z exit you from different angles. Normally observer B only sees image X. You take images V, W, Y, and Z and bend them towards B. Now B sees copies of you at A1, A2, A3, A4. When they look around, it now looks like there are five of you. Note that each copy looks a little different because its from a slightly different angle.

4) Bend light to make something look different.

Example: You want to look taller, so why not.

'Realistic'-wise this might require some rethinking.

Take the example of the person driving a car. The talent can decide whether the car is invisible, the person inside it...what about their clothes? Do they have to specify for every single object in the car, and what counts as an object (is a bottle of water one object, or does it comprise bottle, bottle top, and water)? Do they have to specific for every single molecule, or every atom...?

The atmosphere is touching them, can they make it invisible? What about objects in the atmosphere like clouds, birds or planes? Or objects within or on the Earth, which is within their radius...?

This level of control with require a kind of super-awareness and super-computation power far in excess of any human brain. This will be far more significant than mere invisibility.

In practice, as others have suggested, some kind of mind-altering power so the talent is not noticed is likely to make far more sense than selectively moving individual photons.

A Somebody Else's Problem Field.

Being invisible is definitely really cool. You can go do anything you want, whenever you want, without anybody being able to mess with you. At least as long as you don't have invisible eyelids, that is; then you become your own problem.

However, invisibility does have one problem: no matter how good it is, the Observer Effect dictates that an invisible person will have some effect on the world around them. This generally takes the form of foot-shaped depressions in the grass, or unexplained bumps in the night. Utilized by such greats as Slartibartfast, The Doctor, and the Campaign for Real Time, a S.E.P. Field / Perception Filter causes people to ignore these telltales, making you completely invisible. At least until somebody starts jumping up and down while also blinking really fast.

Realistically speaking, the ability to influence the trajectory of individual photons would not yield the kind of results you are wanting, at least not consistently.

Even worse, the exercise of trying to marry a power like this to reality is, practically speaking, almost impossible.

Bending light around an object so that it was invisible would mean that the powered individual would need to be omniscient, at least specifically with regards to where each observer of the space being manipulated is. The view angle of the observer at each moment that each photon were to enter their retina and then be processed by the brain. This would need to happen for every photon that were to come in contact with the surface of the object, and for every photon that should enter the visual cortex of observers, and what to do with the excess photons? Honestly the issue, while mathematically MIGHT be possible (I only throw this maybe in there because the mathematics of accomplishing this are FAR beyond myself), is so incredibly complicated that it is better off sticking to the "because magic" route if bending light is set in stone as the basis of his powers.

Something like being able to alter the mass of an object so that light simply doesn't interact with it is a little bit closer to what you describe, but even this introduces a whole heap of problems if realism is a sticking point (ie. a massless car disassembles at a molecular level. And even if the forces that hold it together are not effected somehow by its loss of mass, it certainly wouldn't be able to still interact with other physical forces like gravity, and the driver's interaction with those forces).

Light manipulation and some level of mind control.

Initially, the ability to bend light seemed enough. Just with that, you'd already be able to turn yourself and anything else invisible, potentially create a heat beam (concentrate a lot of infrared light on a single point), see better in the dark (force light to keep going back into your eyeballs, thus causing the necessary stimuli to see) and the ability to get a perfect tan. The main problem here was your car example. For light to hit the driver, thus making him visible, while keeping the car invisible, it'd need to go through the car as if it didn't exist, which simply isn't really possible (for the visible light, that is).

However, it could happen, if instead of just light manipulation, your character also had the power to control minds, blocking the information sent by the eyes and plant images on people's heads. That way, you'd be able to make anything invisible simply by making people unable to perceive what you don't want them to. It would also mean you can create illusions, especially if you're also able to induce fake stimuli from other senses, even to the point of making someone believe they're cooking up in a place below 32 Fahrenheit/ 0 celsius. This however would mean that, without light manipulation, you'd be able to avoid detection by guards, but not by the cameras (reminder that if light doesn't hit your eyes, you'll be essentially blind, unless you just deflect the light that reaches the cameras).

Frickin' lasers!

(Sharks not included.)

You need a light source. With selective bending of light, your range sets the radius in which you can capture all the sunlight available, focussing it into a collimated source.

If you can block light, you may also be able to intensify light. This will give you an optical amplifier. Even without that though, you could carry this around with you.

Finally, if you can bend light such that it loops back round on itself again, you have created an optical cavity. Combine this with your optical amplifier, and that gives you all the major ingredients of a laser.

And finally of course you provide the targetting mechanism to place the laser dot on whatever you want to heat up.

I should mention of course that when you're playing with large amounts of energy like this, you would want to be really sure you've got it under control, otherwise you could get a bit more than just sunburn. I would strongly recommend including some kind of shield to deflect all light coming towards you from the laser's location, just in case.

Useful side powers

• Something that allowed them to stay aware of their surroundings. Sonar? Perhaps they can see some part of the spectrum normal people can't, or can shift light into the visible spectrum from other wavelengths. X ray vision.
• Insulation might be handy. Without all the ambient heat save convection, they might get cold after a while. Basically the temperature difference between night and day. This would probably just mean wearing clothes that appeared to be inappropriately warm.

Science/Medicine

Turing parts of something invisible (the ground, a person), but leave the interesting bits visible. What's interesting varies depending on what you're looking for:

• Bullet fragments inside a person during surgery. Imagine an anatomy class taught or assisted by them. Never vivisect again. Instant pregnancy test with gender weeks earlier than a sonogram could manage.
• Tumors/broken bones. No more x-rays or exploratory surgery while they're available.
• Ore
• Oil
• Tunneling animals and insects
• Secret passages
• Fossils
• Help unclog "Morning Glory" (a geyser in Wyoming), and find out why it's so regular.

How valuable would this person's time be? I imagine they'd charge ore/oil all the market could bear, and do lots of charity work for medicine (not all medicine, but yeah) research, etc. Maybe work out some reciprocal agreements for pet projects ("I'll use all your fancy recording and measuring gear over here for my thing, then we'll go use my power[s] and your gear for your thing").

Combat

• Turn someone's retinas invisible, blinding them.
• Invisible cover + piercing projectile = enemy casualty
• Stealth, derp. How many people will fit inside this radius?

Astronomy

• Fly them up to the moon. Have them gradually "remove" layers so we can get a good look at everything, like an MRI of the moon. Or turn all the bland ol' rock invisible and see what else is up there... buried alien listening post? Lots of meteors, certainly.
• Most potential applications moved to "limits", below... because daayymn.

Limits

• How long does the effect last once the object is entirely outside their radius?
• Does a dangling thread count as part of a person? Deliberately unravel a sweater/unspool some wire to keep someone invisible from further away.
• Turning half the earth invisible and exposing the core would allow a lot of radiant heat to escape that would have otherwise been held in. A minutes worth of heat loss might not have a measurable effect, but what happens as the Earth's core starts to cool? Weird new convection currents as a relatively thin section of the mantle cools a bit. "Oops, I just switched the poles... let me do that again to put it back... oh shit (sudden uptick in earthquake activity, and in places one wouldn't normally expect them)".
• Is a city all one thing? In entering a city can they selectively turn various parts invisible? Hold a city hostage by threatening to blind everyone. Or by turning all the street lights, cars, and people invisible.
• Is a solar system all one thing? Removing the light/heat from the sun would be fairly cataclysmic to Earth in the long term. Same result by turning Earth invisible, none of that warming radiation hits us, stuff gets colder. Hey! Combat global warming.
• Is our arm of the galaxy...
• our galaxy...
• our universe...
• our multiverse...

You really need to set limits somewhere. If its something like "contiguous solids and liquids", then they can't affect a mist, or sand, or gravel, but could turn all the oceans invisible.. Or a brick/masonry wall. Hell, human skin could be argued as a contiguous object, while the layers of fat, muscle, organs and bone are different things.

The ability to bend light could make you invisible to the casual observer, but anyone who really wanted to detect you could do so without too much trouble. You see, when you bend light around an obstacle, that bent path is longer than the original straight-line path (a 3-foot radius bubble around you would add almost 3.5 feet to the distance). This means it takes longer for light to travel from point A to point B if it passes through your invisibility field. The human eye likely isn't sensitive enough to pick up this small delay, but any sort of laser-based ranging system would see a measurable discrepancy between its readings and the true distance. These systems bounce a laser off a target like radar. Since the light goes out and back again, your bubble would bend it twice and make the delay even more noticeable. No amount of light bending can compensate for this (you can't create a path that's shorter than the natural straight-line path, and you can't make light go faster).

Your enemies would simply deploy lidar systems. Your invisibility field would show up as a blob-like distortion. You'd be extremely detectable on lidar while moving because objects behind your bubble would appear to suddenly jump away from the viewer, and then suddenly jump back once you left the field of vision. Your enemy would just wait for fixed objects to start moving on the lidar screen and then start shooting in that direction. Someone experienced with digital signal processing can probably combine the feeds from lidar and from a traditional video camera and see through your invisibility to a degree. Add a sonar system into the mix and you can likely eliminate the invisibility completely.

Side note: Your character should never use their powers anywhere near a self-driving car. They rely on cameras and lidar for navigation, and these powers would interfere with that navigation system in a way that's likely to disorient the vehicle and cause an accident.

That's not to say this ability is useless, particularly if you're the creative sort. Carry a few relatively innocuous items around with you and you can do some interesting things.

Any fourth-grade kid knows that you can use a magnifying glass to focus sunlight and heat up objects until they auto-ignite. The ability to bend light means that you can take that magnifying glass and more or less put the lens's focal point wherever you want. You could be a natural archenemy for Ant-Man, or the only hero that's not afraid of Mr. Freeze.

Wear a necklace that has a glass prism on it. Prisms are neat because they can take a beam of white light and split it into individual colors. Once you have sources of monochromatic light, you can create illusions/mirages by bending individual wavelengths differently so that the light forms an image when it reaches the observer. It's like painting, but at the photon level.

Carry around one of those small but unreasonably bright LED flashlights. If you ever need to escape from an attacker, blind/disorient them by flashing it directly into their eyes. Since you can bend light, you can even do this while running away and facing the other direction. Similarly, a pocket mirror can be used to create a sun glare effect that you can bend and redirect to temporarily blind any person or camera.

Speaking of escape, you would be able to disable almost any attacker not just by bending the light around you, but by changing the way that you bend the light in a smooth, cycling pattern. The attacker sees the space in front of him rising and falling, shifting position and orientation as if he was standing on a boat in rough seas. His inner ear claims he's not actually moving, though, and that sort of sensory contradiction can induce dizziness, loss of balance, and the sort of motion sickness that astronauts suffer from.

Simply replace the matter making up your body with "dark matter". Then you don't have to worry about bending light. As I understand it, "dark matter" cannot be detected by any means except gravitationally.

Kaitlyn, heroine of my upcoming series The Vault, can turn invisible via secreting a solution that bends light. It is viscous enough to stick to her skin, while being able to get onto her hair and make it invisible, and it covers her eyes and the insides of her orifices. It's also dirt-repellent, and waterproof. However, she can't see using visible light, and infrared light can be used to see her, so she sees in infrared while invisible.