Ratio of the reflected and transmitted wave to the incident wave are depicted as follows:
where Γ is the reflection coefficient at the boundary between media-1 and 2:
We will derive the ratio of the reflected and transmitted wave to incident wave.
Let 'a1' be a incident wave, 'b1' be a reflected wave and 'a2' be a transmitted wave.
The voltage and current must be continuous at the boundary.
Here note that the sign of backward current is negative.
Eliminating va2, we obtain the ratio of reflected wave to incident wave voltage, which is defined as reflection coefficient Γ.
Noting that Z1,Z2 are positive, the magnitude of the reflection coefficient is less than unity.
The ratio of current is just different from that of voltage in sign.
Therefore the reflection coefficient of power is:
Similarly, eliminating vb1, we obtain the ratio of transmitted wave to the incident wave:
Note that the power flow satisfies the conservation law of energy.