The next day at the hour of sunset Aragorn walked alone in the woods, and his heart was high within

The next day at the hour of sunset Aragorn walked alone in the woods, and his heart was high within him; and he sang, for he was full of hope and the world was fair. And suddenly even as he sang he saw a maiden walking on a greensward among the white stems of the birches; and he halted amazed, thinking that he had strayed into a dream, or else that he had received the gift of the Elf-minstrels, who can make the things of which they sing appear before the eyes of those that listen.

For Aragorn had been singing a part of the Lay of Lúthien which tells of the meeting of Lúthien and Beren in the forest of Neldoreth. And behold! there Lúthien walked before his eyes in Rivendell, clad in a mantle of silver and blue, fair as the twilight in Elven-home; her dark hair strayed in a sudden wind, and her brows were bound with gems like stars.

For a moment Aragorn gazed in silence, but fearing that she would pass away and never be seen again, he called to her crying, Tinúviel, Tinúviel! even as Beren had done in the Elder Days long ago.

Then the maiden turned to him and smiled, and she said: ‘Who are you? And why do you call me by that name?’

And he answered: 'Because I believed you to be indeed Lúthien Tinúviel, of whom I was singing. But if you are not she, then you walk in her likeness.’

'So many have said,’ she answered gravely. 'Yet her name is not mine. Though maybe my doom will be not unlike hers.’

–J.R.R. Tolkien, The Lord of the Rings: The Return of the King, Appendix A, “The Tale of Aragorn and Arwen”