Hey there, recently been studying Optics in Feynman's book vol.1 and came across his geometrical approach of Fermat's least time theorem and its application on refraction. So he illustrates refraction geometrically like this (attached jpeg for those without the book) and so he goes on to say that : "Therefore we see that when we have the right point, XC sin(EXC) = n XC sin(XCF) or, cancelling the common hypotenuse length XC and noting that : EXC = ECN = θ_i (angle) and XCF = BCN' = θ_r (angle) , we have sinθi = n sinθr. However I am trying to figure out why the equivalence in bold stands, and I can't see it. In fact I'm pretty sure it shouldn't be so normally, but Feynman states something about an approximation later on (that the two different paths' travel time should be thought of as equal), so this may be why the angles are so. Anyone care to explain? It may be something really geometrically simple, but it bothers me !