Interesting question.
There are two possible answers that I see, which depend on the state of the lightsaber. I'm going to take some liberties and assume certain things about the workings of the lightsaber based on observable properties of it.
As mentioned elsewhere, if the lightsaber is already on, since the blade is a tube of plasma contained within a magnetic envelope, the blade will simply cut a hole through the mirror and anything behind it (largely because plasma does not give a fuck).
But what happens if you put a deactivated lightsaber up to a mirror and turn it on?
This is where things get incredibly speculative.
First we need to figure out what actually happens when a lightsaber is activated.1
Anyone who's seen a starwars movie can tell you: the lightsaber extends from the base, almost as if the blade were stored in the hilt. Now, one would not be entirely foolish for assuming that the blade plasma is stored in the hilt, generated by some arcane method, and extruded to the containment envelope on activation, but then this raises the question of how lightsabers stay hot during use. The temperature differential between plasma capable of cutting metal like butter and human-survivable atmosphere is akin to the temperature differential between molten glass and liquid nitrogen. So, something has to be re-energizing the plasma while the lightsaber is in use, even if it isn't cutting anything.
The easiest2 way to re-energize a plasma and to create more from an atmosphere3 is a stupidly high-powered laser tuned such that nitrogen/oxygen atmospheres are opaque to it. (This is why we don't see a gigantic fuck-off beam of light blasting out of the end of the lightsaber and igniting things at a distance.)4
So, a lightsaber ignition sequence is as follows:
The magnetic containment envelope flicks on (safety first!)
Immediately afterwards the laser powers on and the beam contacts the air adjacent to the lens. This (for all intents and purposes) instantly ionizes the air and imparts ludicrous amounts of energy into it, thus creating lightsaber plasma.
Whether through simple brownian motion or through a flow actively created by the magnetic containment envelope itself, the plasma disperses away from the point of creation, leaving a void to be filled by regular atmosphere, thus starting the process of plasma creation all over again.
The magnetic envelope fills and the laser now maintains the temperature of the plasma.5
So, now back to the question: What would happen if we put a lightsaber up to a mirror (assuming a perfectly reflective surface) and turned it on?
If you're in an oxygen/nitrogen atmosphere (or the lightsaber has been tuned to the atmosphere you are currently in):
- The lightsaber ignition sequence continues normally, with the initial plasma created by the tiny pocket of air between the lightsaber and the mirror6 providing enough energy to melt a hole through the mirror, thus allowing in more air to complete the ignition sequence.
If you're in a non-oxygen/nitrogen atmosphere (or the lightsaber is not tuned to the atmosphere you are currently in):
The plasma-generation laser passes through the air imparting minimal energy (instead of all/most of its energy) to it, strikes the reflective surface and, depending on the angle the lightsaber is held at, either
- A) passes back into the lightsaber, likely leading to a catastrophic explosion and/or grievous harm to the user
- B) reflects off of the mirror and continues on to cause catastrophic damage to whatever it finally strikes
So, what can we take from this?
Always keep your lightsabers tuned.
Please note, I'm only going to be drawing from the movie canon here. The blaster ammo reference in the 3rd footnote is from a technical guide for the star wars movies, which is a lower order of canon, but still directly related to the movies.
Note: It would be possible to re-energize the plasma through induction created by a properly designed magnetic envelope, but creating new plasma using this method would be rather inefficient, since most atmospheric gases have low interaction with even extremely high-power magnetic fields.A Having separate methods for maintaining and creating plasma when a single system can do both seems incredibly silly, so I applied occam's razor and concluded plasma is both generated and maintained by a properly tuned laser.B
Take note that in the primary canon (the movies) we have never seen a lightsaber used or activated without some kind of atmosphere. According to this theory of lightsabers, they wouldn't work in a vacuum. It can be presumed that blasters create plasma from an internal source, which explains both how they can operate in a vacuum and how they can run out of ammo.
The atmospheric tuning explains a scene in the beginning of The Phantom Menace which is otherwise extremely odd: When quigon and obiwan are sitting in the conference room, sipping their tea, and the room is flooded with poison gas, they don't attempt to cut the door, or even activate their lightsabers until the door is opened thus restoring the air inside the room to an oxygen/nitrogen atmosphere, and allowing the lightsabers to actually perform the ignition sequence instead of acting as overpowered hyper-lethal laser pointers. This also explains why they went straight to holding their breath rather than cutting through the door, as the change in atmosphere would render even an already activated lightsaber useless and likely extremely dangerous.
Note that this theory of lightsabers allows for variable blade plasma temperatures, which explains how in The Phantom Menace quigon could cut through multiple blast doors with a blade so hot that molten metalwas flowing from the hole, while in A New Hope luke could hold the blade inches from his face to examine it without his face catching fire and burning the fuck off. This suggests that a lightsaber has a baseline (likely user customizable) temperature that can be changed on the fly as circumstances require. It would make sense to have the blade idle at a lower temperature, as higher blade temperatures require more energy to maintain and thus presumably allow a shorter span of time before the energy source of the lightsaber is exhausted.C
Closeups of lightsabers that I have seen have the emitter assembly slightly recessed from the outer housing of the hilt, which makes a lot of sense: for the lightsaber's ignition sequence to work there must be atmosphere for the laser to affect, thus a recessed emitter assembly would allow a lightsaber to be activated even while flush against a surface. Even with thicker objects this would allow the full ignition sequence to complete: The initial pocket of air-turned-plasma would burn a small hole into the object, which would create a void which would be filled by atmospheric pressure, which would allow the blade to extend further. Repeat ad-nauseum.
A - This would also generate the entire blade simultaneously, which directly contradicts movie canon. Thus whatever is generating the blade must start from the hilt and work its way up.
B - Note that this would make the part of the lightsaber blade closest to the hilt the hottest, which is supported by The Phantom Menace: The part of the bridge blast door quigon's lightsaber hilt is closest to is noticeably more molten than the far side of the blast doors near the end of the blade.
C - This also allows for variable lengths (extend the containment envelope and increase the laser power (and the flow rate induced by the magnetic envelope, assuming this is the method by which plasma is dispersed)), which explains how in some scenes a lightsaber appears to be as long as an arm, while in others it appears to be nearly 2/3 of the same wielder's height. The same power supply time constraint would apply here in regards to blade length: a longer blade requires more plasma, and thus the laser must do more work to keep a larger volume of plasma at the same temperature. The extensibility of the blade seems to make a compelling argument for an envelope-induced flow of blade plasma, as longer blades would quite quickly have very uneven temperatures, possibly even after accounting for the brownian motion of an extremely energetic plasma (it would be great if a physicist/chemist could run the numbers on this). The arena battle scene with the horde of jedi in Attack of the Clones seems to support the power limitation theory, as the blades of the jedi as they run towards the droids are extremely short, presumably because the jedi are aware that this will be a long confrontation that will require extended lightsaber use, and are thus trying to conserve power.