The rainbow suggests the first covenant between God and man, from the flood story in “Genesis,” and the poem uses the narrator’s reaction to the rainbow to expose the problem with seeing man’s unity to the divine through religious doctrine. As the narrator “leaps up” at an answer outside of himself, he mistranslates his zealous instinct for blessedness. He reveals his mistake through the pride of first person pronouns, the "I am"; the echoes of God's imperative voice, the temporal and mortal view of eternity, omitting the life of the spirit, and the allusion to the Sphinx’s riddle, Oedipus’s pride. His desperation leads to "a spontaneous overflow of powerful feeling”: "Or let me die!" that like the flood, wipes out his first creation, and the rest of the poem reveals the narrator’s resulting humility and realization of truth as he looks inward to and with his imagination.
William Wordsworth was a Nature poet who worshipped Nature as his God. For Wordsworth, Nature was his main source of spirtual comfort and escape from all the cares of this world. His association with life giving and life sustaining Nature began even when he was only a child and remained with him till his death.
In this short lyric, the 'rainbow' symbolizes the life sustaining and life nourishing goodness of Nature. The sight of the beautiful rainbow which he saw when he was only a child is deeply etched in his memory and the same joy that he experienced when he saw it as a child contiunes to remain with him through his adulthood. He desires that this same childhoood joy should continue to sustain him even in his old age. Wordsworth says that he would rather die than not being able to experience the same joy that he experienced when he saw the rainbow when he was a small boy after he becomes an old man.
The memory of the beautiful rainbow and its pleasant associations form the link between his childhood, adulthood and his old age:past, present and future. Wordsworth concludes the poem by expressing the desire that each day of his existence be linked with the next by beautiful and simple natural sights like the rainbow.
The rainbow which he saw when he was a child becomes the 'objective correlative' in the literary text which recalls to his mind the pleasant memories associated with the beautiful rainbow.