Why do waves refract to hit headlands?

I'd suggest that you either look in a book or draw a picture. Draw a wave coming in parallel to a coast that has a bay and headlands. The bay will have deeper water while the headlands has shallow water. The wave moves faster in deep water, and slower in shallow water. That means that the part of the wave near the headlands slows down, while the part near the bay moves faster. What does that do to the wave front? It's just like what happens when you get the wheels of your car off the road into sand or something soft, that side of your car slows down while the other side doesn't, and your car gets turned farther off the road.