In the book: On the eve of the Fellowship’s departure of Lothlórien, Frodo and Sam discuss the apparent magic and beauty of Lórien. Sam says that he wishes he could see “Elf-magic”, but Frodo does not- he states that he is content. Both agree that they would dearly like to see Galadriel again.
At that moment, Galadriel appears, and she beckons that Hobbits- both Frodo and Sam- to follow her. She leads them to an enclosed garden and down a flight of steps to a dell, through which a stream flows. A silver bowl sets on a pedestal carved like a tree, and Galadriel fills this with water from the stream. She tells them that this is the mirror of Galadriel, and that she has brought them here to look in it. Frodo, ever cautious, asks what it is that they will see, to which Galadriel replies, in typical Elf- fashion,

“ Many things I can command that mirror to reveal, and to some I can show what they desire to see. But the mirror will also show things unbidden, and these are often stranger and more profitable than things which we wish to behold. What you will see, if you leave the mirror to work, I cannot tell, for it shows things that were, and things that are, and some things that yet may be. But which it is that he sees even the wisest cannot tell.”

Frodo does not reply to her query, “Do you wish to look?” But Sam, torn between fear and curiosity, says that he’d like to see what he can. Though at first all he sees is stars the mirror soon shows him many more visions: Ted Sandyman, the Hobbiton miller, cutting down trees in the Shire; Frodo, apparently asleep, lying under a cliff and Sam himself climbing up winding stairs and through a dark passage, looking urgently for something; the Old Mill in Hobbiton gone, replaced with a large red brick building; his own father, the Gaffer, turned out of his because Bagshot Row had been dug up. Sam cries out that he must go home at once to help his gaffer, but Galadriel reminds him that he cannot go home alone, and that, ‘You did not wish to go home without your master before you looked in the mirror, ad yet you knew that evil things might well be happening in the Shire…some things [that the Mirror shows] never come to be, unless those that behold tem turn aside from their path to prevent them.”
Frodo looks in the Mirror next. Galadriel answers his question, “Do you advise me to look?” With a, “Do as you will.” Frodo climbs up onto the base of the pedestal and peers into the water. At first he sees a figure, robed in white, walking down a long twilit road, mountains looming in the distance. Frodo cannot tell whether the figure in Saruman or Gandalf; he sees Bilbo walking restlessly about his study, his table littered with papers and rain pounding sown outside; he sees many brief glimpses of what he discerns to be the history of the tale he has become caught up in; then the Sea, rising and raging in a storm, and against a blood-red sunset a ship comes sailing out of the West; a great city with a river flowing through it and beyond; a fortress with seven towers; the ship again but bearing a flag with an emblem of a white tree on it; the sun sinking again into a sky red with battle fire and smoke; and a small, lighted ship sailing away. Finally, he sees the Eye burning out of a black abyss, roving, searching for him. The Ring grows heavy, and begins to drag Frodo down to the surface of the water. When he faces off with Galadriel, the Elf Lady grows “great and terrible”, certainly, but not to the degree of greatness and terribleness that we see in the movie. When Galadriel finally refuses the Ring, she seems to have “shrunk”, and to have become neither frightening nor threatening.

In the Movie: At night (apparently the first and only of the Fellowship’s stay in Lothlórien), Galadriel walks past the Fellowship’s pavilion and down a flight of stairs into a dell. Frodo wakes as she passes, and follows the Elf. Without acknowledging Frodo’s presence, Galadriel fills a silver ewer from a fountain like spring that flows out of the wall of the dell into a small pool, and stands before a tree-like plinth that has a shallow silver basin resting on it. Galadriel asks Frodo if he will look into the mirror. Cautious and unsure, Frodo asks what he’ll see, to which Galadriel replies, “Even the Wisest cannot tell, for the mirror show many things- things that were things that are, and some things…that have not yet come to pass.” As she speaks, Galadriel pours the water from the ewer into the basin, then steps back to regard Frodo. Frodo doesn’t reply, but steps up on the base of the plinth to look into the mirror. The surface of the water ripples as it shows Legolas, Sam, Pippin and Merry looking back at him, as they did earlier on the previous day while awaiting Haldir’s decision. Then he sees a hobbit-hole in the Shire, and hobbit-buildings along a riverfront. The scene abruptly turns to night, and orcs chase hobbits along the waterfront while the buildings burn. Next, a huge, ugly mill belches smoke into a smoggy sky while a line of Hobbits- Sam and Rosie included- are marched to the mill under the lash to work. The Eye of Sauron then appears, dragging Frodo down towards the water under the weight of the Ring. He struggles, then tears the chain from around his neck and falls to the ground. Frodo picks himself up and looks apprehensively at Galadriel, who returns his look calmly. She tells him, “I know what it is you saw, for it is also in my mind,” then, Frodo hears her voice in his mind, “It is what will come to pass, if you should fail. The Fellowship is breaking. It has already begun. He will try to take the Ring- you know of whom I speak. One by one it will destroy them all!” Frodo’s eyes grow wide with astonishment and fear, and he holds out the Ring, offering it to Galadriel, who reaches out for it, then draws back. Growing suddenly huge and fierce, she towers over Frodo, appearing as a warrior- queen, and cries out in a great voice what would happen if she were to accept the Ring: “On place of a Dark Lord, you would have a Queen! Not dark but beautiful and terrible as the dawn! Treacherous as the Sea! Stronger than the foundations of the Earth! All shall love me and despair! Then, shuddering, she lowers her arms, and, turning, away, refuses the Ring. Frodo says that he can’t complete his task by himself, and Galadriel replies that to bear a Ring “Is to be alone.” She shows him her own Ring then, Nenya and tells him that even though he is afraid, “Even the smallest person can change the course of the future.”

Why the scene was altered:
In the commentary, Phillipa Boyens states that Sam was removed, giving the scene entirely to Frodo and Galadriel, because of how crucial a moment it is for Frodo. The visuals we get in the movie, absent from the book- such as the images of the Fellowship watching Frodo, and the scouring of the Shire, poignantly drive home two points: The concept that Frodo will be the death of the Fellowship if he stays (so Phillipa Boyens) and the consequences of the Quest’s failure: the destruction of Frodo’s home. Overall, the scene was shortened and intensified because of the overall changes that were made to the Lothlórien sequence: In the book, Lothlórien is a complete haven, free of any danger or fear; in the movie, Galadriel presents a psychological threat to the Fellowship.