The chief of his other contributions to optics was the explanation of the rainbow - an explanation far from complete, since the unequal refrangibility of the rays of light was yet undiscovered - but a decided advance upon his predecessors, notably on the De radiis visas et lucis (1611) of Marc-Antonio de Dominis, archbishop of Spalato.
The path of a ray from the wave-surface A 0 B 0 to the point A is changed; but in virtue of the minimum property the change may be neglected in calculating the optical distance,as it influences the result by quantities of the second order only in the changes of refrangibility.
B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.
This shows that the connexion between the refrangibility of light and its wave-length does not obey any simple law, but depends on the nature of the refracting medium.
This, however, is not the case with ordinary refracting media, the refrangibility generally increasing more and more rapidly as the wave-length diminishes.