Act 1 scene 3
Richard does not have the courage to let the joust determine which of the two accusers is in the right. If Bolingbroke won, it would be a direct attack against Richard himself. And since Richard knows that Mowbray did kill Gloucester at his behest, and since it is in his best interest to believe in God's intervention in men's lives, because his own right to the throne is based on the divine right of kings, he probably believed that God would fight on Bolingbroke's side. But another piece of evidence that Mowbray really was guilty is that Richard banishes Mowbray forever, and Bolingbroke for 10 years, later shortened to 6 years. Richard also is saying he believes both men were exercising their ambition (eagle-winged pride), and therefore he banishes them. He says he is avoiding civil war.
Bolingbroke can also use the Renaissance Christian Humanist language associating sun/king in a prophetic statement that he will be the sun someday. The sun is the metaphor for the kingship in this play, here only lent, not given, to Richard. But Shakespeare want to make him ambiguous here, not clearly telling us his motivation.
Mowbray is understandably surprised by Richard's pronouncement if he was acting under Richard's orders to kill Gloucester. But it is also a judicious move because someone who is willing to kill the heir to the throne might also be willing to kill the king himself.
This speech shows the power of the breath of kings, his pronouncements which can shorten a banishment by 4 years.
Gaunt reminds Richard that though he has a lot of power as king, there are some things that even kings are not in control of.
Gaunt raises the idea that perception affects experience, that what Bolingbroke expects during his banishment will be a self-fulfilling prophesy and that is the way he will experience it. Bolingbroke cannot create that rosey view of his banishment. This interchange reinforces the conflict between father and son, especially in the differing views they have of the world.
Gaunt refers to the jewel against a dull background to suggest that Bolingbroke's return will shine brighter because of his unhappiness of his experiences abroad. Gaunt will later refer to the "precious stone set in the silver sea" in his Royal Throne of Kings speech in 2.1 refering to England as another instance of this same metaphor. Gaunt refers symbolically to the value of a jewel being like the happiness of Bolingbroke's return, but Bolingbroke uses the same term as representative of the value of what he is forced to leave. But it could also refer to the crown jewels, which his ambition seeks, but which he cannot hope to accomplish if he is forced to live outside of England.
Again, Bolingbroke is not capable of using his imagination to change or interpret his condition. This marks him as more of a Machiavellian, the scientist who sees things as they are.