Como o Espelho de Galadriel obteve o poder de mostrar visões?

Magia.

Isso soa como uma resposta faceta, mas na verdade não é. Ao introduzir o Mirror, Galadriel chama a menção anterior de Sam de "Elf-magic":

'And you?' [Galadriel] said, turning to Sam. 'For this is what your folk would call magic. I believe; though I do not understand clearly what they mean; and they seem also to use the same word of the deceits of the Enemy. But this, if you will, is the magic of Galadriel. Did you not say that you wished to see Elf-magic?'

^{Fellowship of the Ring Book II Chapter 7: "The Mirror of Galadriel"}

Tolkien refere-se a esta passagem (obliquamente) na carta não enviada 155, quando fala sobre os diferentes tipos de magia em seu mundo (ênfase dele):

I suppose that, for the purposes of the tale, some would say that there is a latent distinction such as once was called the distinction between magia and goeteia. Galadriel speaks of the 'deceits of the Enemy'. Well enough, but magia could be, was, held good (per se), and goeteia bad. Neither is, in this tale, good or bad (per se), but only by motive or purpose or use.

[...]

Their magia the Elves and Gandalf use (sparingly): a magia, producing real results (like fire in a wet faggot) for specific beneficent purposes. Their goetic effects are entirely artistic and not intended to deceive: they never deceive Elves (but may deceive or bewilder unaware Men) since the difference is to them as clear as the difference to us between fiction, painting, and sculpture, and 'life'.

^{The Letters of J.R.R. Tolkien 155: To Naomi Mitchison (draft). September 1954}

Se o Mirror é um magia ou um efeito goético, é claro que é produzido por "magia" élfica.

O Espelho não aparece em nenhum outro texto de Tolkien, e nenhum de seus primeiros rascunhos do capítulo o aborda em grande detalhe, então isso é o melhor que podemos fazer.

Podemos fazer uma comparação interessante para o palantíri ¹ , também feito pelos elfos. Embora eles funcionassem mais como telescópios do que o espelho do Galadriel's Mirror, eles podiam ver a maioria dos eventos em qualquer lugar do mundo:

The vision of the palantíri was not "blinded" or "occluded" by physical obstacles, but only by darkness; so they could look through a mountain as they could look through a patch of dark or shadow, but see nothing within that did not receive some light. They could see through walls but see nothing within rooms, caves, or vaults unless some light fell on it; and they could not themselves provide or project light.

^{Unfinished Tales Part 4 Chapter III: "The Palantíri"}

E Gandalf sugere que eles também poderiam ser usados para ver através do tempo (negrito é minha ênfase, itálico é de Tolkien):

'Each palantír replied to each, but all those in Gondor were ever open to the view of Osgiliath. Now it appears that, as the rock of Orthanc has withstood the storms of time, so there the palantír of that tower has remained. But alone it could do nothing but see small images of things far off and days remote. Very useful, no doubt, that was to Saruman; yet it seems that he was not content. Further and further abroad he gazed, until he cast his gaze upon Barad-dûr. Then he was caught!

[...]

And how it draws one to itself! Have I not felt it? Even now my heart desires to test my will upon it, to see if I could not wrench it from him and turn it where I would - to look across the wide seas of water and of time to Tirion the Fair, and perceive the unimaginable hand and mind of Fëanor at their work, while both the White Tree and the Golden were in flower!' He sighed and fell silent.

^{The Two Towers Book III Chapter 11: "The Palantír"}

¹ Hat-tip para Deer Hunter por sugerir a comparação

Os elfos têm a capacidade de criar dispositivos para tornar suas habilidades mais fáceis de serem executadas e mais rápidas. No mundo de Tolkien, a magia é pensada para manifestação em quase um instante, como Gandalf acendendo um fogo. Elfos, diz-se, podem criar coisas mais de acordo com suas imaginações do que os Homens [Letters of J.R.R. Tolkien]. Os poderes dos espelhos vêm de Galadriel, assim como o Um obtém seus poderes de Sauron, e os outros Anéis de poder dos Elfos, os Palantiri de Fëanor e o manto escuro de Lúthien adquiriram seus poderes dela.