Galadriel after Frodo offers her The Ring….
Galadriel laughed with a sudden clear laugh. ‘Wise the Lady Galadriel may be,’ she said, ‘yet here she has met her match in courtesy. Gently are you revenged for my testing of your heart at our first meeting. You begin to see with a keen eye. I do not deny that my heart has greatly desired to ask what you offer. For many long years I had pondered what I might do, should the Great Ring come into my hands, and behold! it was brought within my grasp. The evil that was devised long ago works on in many ways, whether Sauron himself stands or falls. Would not that have been a noble deed to set to the credit of his Ring, if I had taken it by force or fear from my guest?
‘And now at last it comes. You will give me the Ring freely! In place of the Dark Lord you will set up a Queen. And I shall not be dark, but beautiful and terrible as the Morning and the Night! Fair as the Sea and the Sun and the Snow upon the Mountain! Dreadful as the Storm and the Lightning! Stronger than the foundations of the earth. All shall love me and despair!’
She lifted up her hand and from the ring that she wore there issued a great light that illumined her alone and left all else dark. She stood before Frodo seeming now tall beyond measurement, and beautiful beyond enduring, terrible and worshipful. Then she let her hand fall, and the light faded, and suddenly she laughed again, and lo! she was shrunken: a slender elf-woman, clad in simple white, whose gentle voice was soft and sad.
‘I pass the test,’ she said. ‘I will diminish, and go into the West, and remain Galadriel.’
With Galadriel when she gives gifts to the Fellowship…
’“…Ring-bearer,’ she said, turning to Frodo. ‘I come to you last who are not last in my thoughts. For you I have prepared this.’ She held up a small crystal phial: it glittered as she moved it, and rays of white light sprang from her hand. ‘In this phial,’ she said, ‘is caught the light of Eärendil’s star, set amid the waters of my fountain. It will shine still brighter when night is about you. May it be a light to you in dark places, when all other lights go out. Remember Galadriel and her Mirror!’ Frodo took the phial, and for a moment as it shone between them, he saw her again standing like a queen, great and beautiful, but no longer terrible. He bowed, but found no words to say.”
Later in Sam’s fight with Shelob….
“A Elbereth Gilthoniel
o menel palan-diriel,
le nallon sí di’nguruthos!
A tiro nin, Fanuilos!
And with that he staggered to his feet and was Samwise the hobbit, Hamfast’s son, again. ‘Now come, you filth!’ he cried. ‘You’ve hurt my master, you brute, and you’ll pay for it. We’re going on; but we’ll settle with you first. Come on, and taste it again!’ As if his indomitable spirit had set its potency in motion, the glass blazed suddenly like a white torch in his hand. It flamed like a star that leaping from the firmament sears the dark air with intolerable light. No such terror out of heaven had ever burned in Shelob’s face before. The beams of it entered into her wounded head and scored it with unbearable pain, and the dreadful infection of light spread from eye to eye. She fell back beating the air with her forelegs, her sight blasted by inner lightnings, her mind in agony. Then turning her maimed head away, she rolled aside and began to crawl, claw by claw, towards the opening in the dark cliff behind.”
J.R.R. Tolkien, The Lord of the Rings
Why is it important for Frodo to “remember Galadriel and her Mirror”?