The construction in Fig. P.4.12 corresponds to Descartess erroneous derivation of the Law of Refraction. Light moves

Question:

The construction in Fig. P.4.12 corresponds to Descartes€™s erroneous derivation of the Law of Refraction. Light moves from S to O in the same time it travels from O to P. Moreover, its transverse momentum is unchanged on traversing the interface. Use all of this to €œderive€ Snell€™s Law.

Fig P.4.12