Hi all, I'm after a little guidance for I do not know what is going wrong. I understand that for Johann Bernoulli's proof of the brachistochrone problem he used refraction of light and Fermat's principle of least time. I have decided to do a project on the subject, in which I am dividing up a vertical displacement into media of differing refractive index as a function of velocity (for this example, lets say 10m into 10 sections 1m in height). With this I am finding the velocity of an object at each point by of crossover: v = sqrt(2gy) and then plugging the values in velocity into Snell's law to find the angle at which the path changes at each change in medium. Now, for the first first change (at Δy = 1) the equation works out to be sinΘ2 = (v2sinΘ1)/(v1) But as the velocity is ever increasing at each point is always sinΘ2 > 1 Which obviously cannot be right. So where is it I am going wrong? Thanks in advance.