When my book derives equations for reflection between two media it simply says something like this: Suppose a plane electromagnetic wave meets the boundary between two media. This gives rise to an incident and a reflected wave. But I am always puzzled. What is that states that there MUST be reflection? I mean a transmitted wave is also a solution to the wave equation so why can't a transmitted wave without a reflected wave be just as good as a solution. To sum up, it just all seems like guesswork to me.