As I stated in my post, you can certainly increase the exposure time by coating it with a mirrored coating, but the performance trade off isn't as good as you'd like to think. Even if you managed to get 100% reflection with your mirror, something as small as a mote or a crack can still ruin the surface and render it vulnerable to laser.
As I said, its not hard to find 99.9% reflective mirrors even on the civilian market. You would expect military spec'd mirror shields to at a minimum match that, if not be much more effective.
However, since there is precious little literature on just how effective military grade mirror shields could be, I just used the civilian one as a benchmark example.
The nature of the two technologies also favours the mirror shield, as it would be much easier to make a better material able to reflect a higher percentage of the laser's energy than it would be to raise the power of lasers enough to offset that improvement in the mirror shield.
In addition, I said its not about immunity, but rather about buying time.
Even with a mote, first your laser has to rely on blind chance to hit that mote of dust (which is unlikely to stick around on a missile cone flying at M2-3, but we will allow it for argument sake) on the missile's surface, its only a tiny fraction of the laser beam that is hitting that tiny mote of dust, so its going to take many times longer to overcome the mirror shield. Although under such a scenario, the speed of damage is going to increase exponentially as the burnt area increases in size.
Another point I forgot to raise is the fact that most mirrors are only designed to reflect a narrow band of electromagnetic frequencies well (for household purposes, visible light). UV lasers can easily defeat a mirror optimized for lower frequencies.
True enough, but the laws of physics means that any decent scientist would be able to hazard a very accurate guess as to the operating frequency of a particular laser from just its operating characteristics.
And once again the nature of the technology comes in, whereby it is an order of magnitude easier, quicker and cheaper to develop a new mirror shield optimised to enemy laser frequencies than it would be to develop a new laser operating to a different enough frequency to bypass existing mirror shields (if that is even possible given the finite number of frequencies suitable to use for direct kill laser weapons).
You could potentially even design coatings able to deal with multiple, vastly different wavelength lasers by applying a layered design of several coats optimised against different frequency lasers.
The layers are designed to burn off cleanly and insulated from underlying layers to ensure the undercoat is not damaged if the surface layer is burnt off by a laser frequency it was not optimised against.
At which point the newly revealed layer, which is specially optimised to the laser in question, start reflecting the overwhelming majority of the incoming laser energy away, buying your missile the extra few minutes or seconds it needs to punch through laser based interceptor technology and hit their intended targets.
