Let vi be the velocity of light in air, and vz be the velocity of light...

  

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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. А 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 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. А 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