Which expression correctly defines the reflection coefficient at normal incidence between two media with impedances Z1 and Z2?

• A. [(Z2 + Z1)/(Z2 - Z1)]^2
• B. [(Z2 - Z1)/(Z2 + Z1)]^2
• C. (Z2 - Z1)/(Z2 + Z1)
• D. 4 Z1 Z2 /(Z1 + Z2)^2

Answer: (B)

At normal incidence, how much of the wave is reflected depends on the impedance contrast between the two media. The ratio of the reflected to incident wave amplitudes is (Z2 − Z1)/(Z2 + Z1). If you want the fraction of incident power reflected, you square that amplitude ratio, giving [(Z2 − Z1)/(Z2 + Z1)]^2. This is the power reflection coefficient for real impedances, which is why this expression is the best choice. The other options either use the amplitude ratio without squaring, take a reciprocal, or describe the transmitted (not reflected) power, which is 4 Z1 Z2/(Z1 + Z2)^2.