"Put on your red shoes and dance the blues."
The eye of Ra represents the right eye, and the eye of Horus the left eye. Ra is the sun god, whose power of vision is thus unlimited, his eye is called “the eye that sees everything” (think Project Looking Glass). The eye of Horus is seen more as a limited power whose protection is mostly linked to physical integrity.
Note that one might introduce the complicating principle of "the mirror." Up is down, left is right. So maybe left-eye symbolism = Right-eye symbolism = The Eye of Providence?