Let vi be the velocity of light in air, and vz be the velocity of light in water. Consider a beam of light traveling from A (a point in the air) to B (a point in the water) through P (a point on the surface of the water), as shown below. a, b and d are constants. a d - x P B 1. Write down a formula for f (x), the time it takes for light to travel from A to B through P. 2. (a) Calculate f'(x). (b) Explain why f(x) has a critical point when sin(a) sin(8) sin(a) sin(8) (c) Explain why f(x) is minimized when