The next war will be fought with lasers beside computers, I'm wondering could a bullet proof vest coated with a highly reflective surface protects user from laser blast. The laser in question is similar to those used in Sci-fi movies such as Star Trek, etc, meaning the output is mainly electromagnetic radiation not hot gas such as plasma.
Mirror only means that laser beam is reflected as a beam. On dense battlefield that's exactly what you want to avoid, because it would be even more deadly than traditional ricochet. No go for mirrors.
What you want is just white, as bright you can get it, to reflect light in all directions, making it less threatening to other soldiers. And you need it to stay white. Heat your armor absorbs, because it will absorb some, must be distributed and dissipated fast. If it can't, black burn marks are not acceptable. Ash must be white, too.
If exposure to laser is too long, you need insulation, so hot outer layer will not burn your guy. And some kind of alarm. If he can't feel he's being shot, he can't get out of the line.
For adaptive, adjustable mirrors, it's also not quite possible, or at least hard.
Speed of light in air is so close to speed in vacuum that difference can be ignored for all practical purposes. So you get information about being fired upon at the moment you are hit. So making decisions then is already a bit late. You would need to track enemy's muzzles before they will shoot to help that. In a crowded battlefield, it's next to impossible - or the technology needed is a game changer on it's own.
Burning is not immediate, that's right. This might give you a moment to adjust, but of course your enemy will do his best to burn you faster than you can adjust. Arms race. But it's easier to increase raw power than to increase computer speed. For ships, this might work. For "bullet proof vest" analog? I can't believe it.
And, of course, computer and servos would take space, making armor more bulky.
If you are using your lasers offensively to burn holes in targets, mirrors in general would work really well as a defense. With that said, there are some caveats you need to consider.
A mirror may not reflect all laser wavelengths of electro-magnetic photons/radiation. Reflective Mylar is fine against visible light but not so good against an x-ray laser. When we think of mirrors we assume visible light. The EM spectrum is much larger than just what we can see.
Even the best mirrors do not reflect 100% of all radiation; some of the energy will still heat and eventually burn through the mirror. This is the equivalent of bashing a suit of armor long enough you finally pierce it. So your mirrors need to have the ability to transfer heat away from the surface and get rid of it somehow. One method of countering this problem is to use a disposable shield/mirror. Aluminum foil chaff between you and your attacker, vaporized water, smoke, or anything that might reflect/disperse/distort/refract the laser will reduce its effectiveness.
If you want to be able see your enemy so you can shoot back, you need holes in your armor for cameras or whatever. Or possibly laser muzzles to shoot back with. Those become vulnerable non-mirrored surfaces to aim a laser at. Using a laser as a weapon will allow precise correction of aim if you are slightly missing a vulnerable spot.
Any inefficiencies in the laser weapon will result in waste heat when running the laser. If this waste heat is large enough (even a small percentage of a powerful enough laser could be a serious problem) the attacker needs to somehow deal with this excess heat if they don't want their weapon to destroy itself.
And even though lasers are not all that bulky or heavy, unless you have a really large battery or a long extension cord, providing power to a powerful laser is a problem. This is why laser weapons are currently restricted to stationary bases or ships that have fission reactors aboard so that the power to run them is close at hand. The problem with mobile lasers is not the laser, it's the power-plant-on-a-railroad you have to haul with you to run it.
Possibly better than a mirror - which is just going to bounce the beam off in what may be an undesirable direction, like towards your friends - might be plates of corner cube reflectors (like the ones used for bicycle reflectors, or the distance measuring reflectors apollo left on the moon.
The corner cube design reflects the beam back in the direction it came from.
Far better are materials that can simply absorb the thermal energy, ablate and allow you to ignore it.
Covering drones or missiles, that already have a very low radar cross-section, with the kinds of tiles found on reentry vehicles like the various space shuttles, typically ceramics and/or aerogels is far cheaper than reflecting surfaces. Additionally rotating the missile at high speed reduces the time any laser has to heat some part of it. Additionally, these tend to be extremely lightweight although brittle and so add little to the weight of the weapon making them an ideal and cheap countermeasure to any maser/laser.
Lasers are easy to counter. The latest fashion for them ignores their obvious limitations in favor of the PR and status they present rather than their efficacy.
A mirror or reflective surface would help. But it will never protect you fully.
Basically the worst you can do is wear something that scatters the laser light in a direction of allies. Like DON'T wear white. It will not scatter enough to protect people from being blinded. Which honestly is the biggest danger for humans on the battlefield. A narrow laser will still spread a lot on a battlefield. It will require a lot to still have a sufficient impact on a singel target.
With less effort you can basically blind the entire enemy army in a short period of time. Making them easy targets. It is extremely unethical way of fighting but would be the most efficient way of use of laser in combat.
If the laser has a fixed frequency, and the enemy knows what it is, then certain materials may be very effective at reflecting or dispersing it. For instance, a very effective defense against a visible-to-IR laser would be a water balloon. Water vapor absorbs visible frequencies quite effectively, which is why clouds are opaque and white. I would want a kind of armor with a layer of pressurized water pockets, with a thin black skin holding it in. When the skin is burned off, the water shoots out of the hole, creating a small jet, which is then vaporized by the laser into a cloud. The cloud will absorb and disperse the beam in all directions, which is about as good as you can get. The laser ends up creating steam outside your body instead of inside.
On the other hand, if the enemy is using Free Electron Laser technology, then they can tune the output to any desired frequency (well, from microwaves through X-rays, which is enough to ruin your day). If the enemy is shooting you with an X-ray laser, you are having a very bad day indeed. There are no good materials to produce an X-ray mirror. The sharpest angle at which you can get full reflection is 2.4 degrees. That means if you want to deflect an X-ray beam 90 degrees (from straight-on to totally sideways), you need 38 of these mirrors all aligned exactly 2.4 degrees from each other, with the beam exactly hitting the first mirror at the correct angle. If you're thinking of making a suit of armor with lots of these "mirror cups" attached to it, don't bother. You'll have the wrong angle for the vast majority of shots, and will just end up changing which one of your internal organs gets sliced up by the beam. I suppose you could make a suit that is 38 layers thick, with gold mirrors angled at 87.6 degrees from normal on the first layer, and getting shallower by 2.4 degrees each layer as you go inwards. However, these X-ray mirror layers need to be made of gold or iridium, which aren't exactly abundant.
Everyone knows about mirrors. The people who make laser weapons know about mirrors, just as the people who make bullets know about bullet-proof vests.
If a laser can be negated by simple armor, it will not be used as a weapon. So any lasers which are carried will have a reasonable chance against any armor they are likely to encounter. Most likely, by having adjustable wavelength, or wavelengths which are difficult to reflect.
It is not "light" that you want to protect against so much as the heat that is absorbed from the light. Most mirrors still absorb upwards of 50% of the photonic energy that hits them meaning a High Energy Laser can often burn through them just as easily as many other materials.
The best substance to reinforce modern body armor with against lasers is actually not reflective at all. Starlite, is a thin polymer coating that can be painted onto nearly any surface that resists lasers in excess of 10,000 degrees Celsius without transferring any noticeable amount of heat through the medium.
The best part is that it turns black when activated so not only is it preventing you from getting burned, but it's also preventing your armor from scattering a bunch of blinding light towards your allies as other answers have pointed out as a problem