When a wave hits a boundary and reflects, it bounces back into the original medium with its frequency and speed unchanged. Its direction reverses, and depending on the type of boundary, the wave may also flip upside down. These core changes apply to all waves: light, sound, water, and vibrations on a string.
The Law of Reflection
Every reflected wave follows one simple rule: the angle it arrives at equals the angle it leaves at. Both angles are measured from an imaginary line drawn straight out from the surface at the point of contact, called the normal. If a light beam hits a mirror at 30 degrees from the normal, it reflects at exactly 30 degrees on the other side. This holds true for any wave hitting any smooth surface.
What Stays the Same
A reflected wave keeps three properties intact as long as it stays in the same medium. Its frequency doesn’t change, because frequency is set by whatever originally created the wave, not by the surface it bounces off. Its wavelength stays the same too, and so does its speed. Wave speed depends entirely on the medium the wave travels through (the density of the air, the tension in a rope, the temperature of the water), not on anything about the wave itself. A high-pitched sound and a low-pitched sound both travel at the same speed in the same room, and both reflect without changing speed.
What Does Change: Phase and Direction
Direction is the most obvious change. The wave reverses course, heading back the way it came (at the angle dictated by the law of reflection). But something less visible also happens at certain boundaries: the wave can flip its shape.
When a wave hits a fixed, rigid boundary, like a rope tied firmly to a wall, the reflected wave flips 180 degrees. A crest becomes a trough, and a trough becomes a crest. This is called a phase inversion. The same thing happens when light traveling through air reflects off a denser material like glass: the reflected light wave inverts.
When a wave hits a free or loose boundary, like a rope attached to a ring that can slide freely up and down a pole, no flip occurs. The wave bounces back right-side up, with crests still as crests. Whether the reflected wave inverts depends entirely on whether it’s hitting something more rigid (denser, stiffer) or less rigid than its own medium.
Energy and Amplitude at the Boundary
Reflection rarely captures 100% of the wave’s energy. When a wave meets a boundary between two different materials, some energy reflects and some passes through (transmits). The split depends on how different the two materials are in a property called impedance, which combines a material’s density with the speed waves travel through it.
When impedance is very similar on both sides of the boundary, most energy passes through and very little reflects. When impedance is vastly different, almost all energy reflects. The fraction of energy reflected follows a precise relationship: it equals the squared difference in impedance divided by the squared sum of impedance of the two materials. In practical terms, this means a sound wave hitting a boundary between bone and soft tissue reflects about 30% of its energy, while a sound wave hitting a boundary between tissue and air reflects nearly everything.
Because some energy is always lost to the transmitted wave (or absorbed as heat), the reflected wave’s amplitude is typically smaller than the original. A quieter echo, a dimmer reflection. The only exception is when the impedance mismatch is extreme enough to reflect virtually all the energy back, as happens with total internal reflection of light.
Smooth Surfaces vs. Rough Surfaces
The texture of the reflecting surface determines whether a wave bounces back in an orderly way or scatters in every direction. A smooth surface, one whose bumps and imperfections are smaller than the wavelength of the incoming wave, produces specular reflection. All the reflected waves leave at the same angle, creating a clear, mirror-like image. This is how mirrors, calm lakes, and polished metal work.
A rough surface produces diffuse reflection. Each tiny section of the surface faces a slightly different direction, so the incoming wave reflects at many different angles simultaneously. The law of reflection still holds at each individual point, but the overall effect is scattered light (or sound) heading in all directions. This is why you can see a rough wall from any angle but can only see a mirror’s image from certain positions. Most objects around you reflect light diffusely.
Standing Waves From Reflection
One of the most striking consequences of reflection is the formation of standing waves. When a wave reflects back along the same path it came from, the outgoing and returning waves overlap and interfere with each other. At certain points, the two waves always cancel out, creating spots called nodes where there’s no movement at all. At other points, the two waves always reinforce each other, creating antinodes where the wave oscillates with double the amplitude of either individual wave.
The result is a wave pattern that appears to stand still rather than travel. The nodes stay locked in place and the antinodes pulse up and down between them. This is how guitar strings, organ pipes, and microwave ovens work: waves bouncing back and forth between boundaries create predictable, stable patterns of energy.
Total Internal Reflection
Under specific conditions, a wave can reflect completely with zero energy lost to transmission. For light, this happens when it travels from a denser material (like glass or water) into a less dense material (like air) and hits the boundary at a steep enough angle. Beyond a specific angle, called the critical angle, the light can’t exit and bounces back entirely. The critical angle depends on the ratio of the two materials’ optical densities.
For glass surrounded by air, the critical angle is about 42 degrees. Any light hitting the glass-air boundary at a steeper angle than this reflects perfectly. Fiber optic cables use this principle to carry light signals over hundreds of kilometers with minimal loss. It’s also the reason you see a mirror-like sheen on the surface of a swimming pool when you look up from underwater at a low angle.
How Reflection Creates Ultrasound Images
Medical ultrasound is essentially a practical application of wave reflection. A device sends sound waves into the body, and those waves partially reflect every time they cross a boundary between tissues with different densities. The device listens for returning echoes, measuring how long they took to come back and how strong they are.
Boundaries between very different tissues, like soft tissue and bone, produce strong echoes (about 30% of the energy reflects). Boundaries between similar soft tissues, like fat and kidney, produce faint echoes of around 1%. The machine assembles these echo patterns into an image. Boundaries with air reflect almost everything, which is why ultrasound gel is applied to the skin: it eliminates the air gap between the probe and the body that would otherwise bounce back nearly all the sound before it entered the tissue.