If the speeds of two media are identical, which statement is true?

• A. No refraction will take place and the angle of incidence equals the angle of transmission.
• B. Refraction occurs and the transmitted angle is different from the incident angle.
• C. Reflection is guaranteed to occur.
• D. The wave changes frequency across the boundary.

Answer: (A)

The key idea is that refraction depends on a change in wave speed across the boundary. If the speeds in the two media are identical, there is no speed change at the boundary, so the wave doesn’t bend. Snell’s law shows that if v1 = v2, then the refracted angle must equal the incident angle, meaning the angle of transmission equals the angle of incidence.

Frequency, on the other hand, remains the same when a wave crosses a stationary boundary. Since the boundary doesn’t move, nothing forces the frequency to change; with the speeds equal, the wavelength stays the same as well (lambda = v/f with v unchanged, so f stays the same).

Reflection is not guaranteed here; if the media are matched in their impedance, there is little to no reflection. The statement about a different transmitted angle is incorrect because, with equal speeds, there’s no refraction to cause bending. The statement about frequency changing is also incorrect for the same reason.