(Snell's Law) Let v be the velocity of light in air and w be the velocity of light in water. According to Fermat's principle, a ray of light will travel from a point A in the air to a point B in the water by a path ACB that minimizes the time taken. Find the ratio

$\dfrac{\sin (\theta _1)}{\sin (\theta _2)}$

in terms of v and w.