Reflection is the process by which a wave encounters a boundary or interface and is redirected back into the region from which it came. Reflection occurs with many forms of waves, including light, sound, radio waves, microwaves, water waves and seismic waves. For a simple specular reflection from a smooth boundary, the angle of reflection equals the angle of incidence, with both angles measured relative to the normal to the surface.
The incident wave, reflected wave and surface normal lie in the same plane under the standard idealised description. Reflection does not necessarily mean that all of the wave energy returns. At a real interface, some energy can be transmitted into another medium, absorbed, scattered or converted into other forms, depending on the material properties and wave frequency. The amount reflected therefore depends on the boundary conditions and physical characteristics of both the wave and the interacting surface or interface.
Smooth and rough surfaces produce different forms of reflection. Specular reflection occurs when a surface is sufficiently smooth on the relevant wavelength scale, so a relatively well defined reflected direction results. A polished mirror provides a familiar optical example. Diffuse reflection occurs when surface irregularities have dimensions or variations that significantly alter the directions of reflected waves, causing energy to spread over many directions.
A painted wall can diffusely reflect visible light, allowing the surface to be seen from many positions even though it does not form a sharp mirror image. The distinction depends on wavelength rather than simply on whether a surface appears smooth to human touch. A surface that is smooth for long wavelength radio waves can be rough for visible light, while a surface that appears rough to the eye may be comparatively smooth for a much longer wavelength electromagnetic signal.
In optics, reflection is governed by electromagnetic boundary conditions. When an electromagnetic wave reaches an interface between materials with different optical properties, the electric and magnetic fields must satisfy specific continuity relationships at the boundary. These conditions determine the amplitudes and phases of reflected and transmitted waves. The Fresnel equations quantify reflection and transmission for different polarisations and angles of incidence.
At normal incidence, the reflected amplitude depends on the refractive indices of the two media, while at oblique incidence the response differs for s and p polarisations. At a particular angle called the Brewster angle, p polarised light can have zero reflected amplitude for an ideal interface between suitable nonabsorbing media. These details explain why reflection can change both the intensity and polarisation state of light.
Total internal reflection occurs when a wave travelling inside a higher refractive index medium reaches a boundary with a lower refractive index medium at an angle greater than the critical angle. Under the ideal optical model, the wave is then completely reflected rather than producing an ordinary propagating transmitted ray in the second medium. The critical angle satisfies sin theta c equals n2 divided by n1 when n1 is greater than n2.
Total internal reflection is fundamental to optical fibres, where light can be guided over long distances through repeated internal reflections under suitable conditions. It is also exploited in prisms and various optical instruments. Even in total internal reflection, the electromagnetic field extends a short distance into the lower index medium as an evanescent field, so the ideal ray description does not represent the entire electromagnetic behaviour.
Sound reflection is responsible for echoes and reverberation. When sound waves encounter a large hard surface, part of their acoustic energy can return towards the source or another region. If the reflected sound arrives sufficiently later than the direct sound, a listener may perceive a distinct echo. When many reflections arrive closely spaced in time, they contribute to reverberation, which affects the perceived acoustic character of rooms, halls and other enclosed spaces.
The strength and timing of acoustic reflection depend on surface size, shape, material absorption and scattering, as well as sound frequency. Large hard surfaces generally reflect more acoustic energy than soft porous materials, which can absorb substantial energy. Architectural acoustics therefore uses controlled reflection and absorption to achieve appropriate speech intelligibility, music quality and sound isolation.
Reflection is not limited to ordinary visible mirrors. Radar systems depend on electromagnetic waves being reflected or scattered by objects, allowing information about range, position and motion to be inferred from returned signals. Sonar uses reflected sound waves to detect underwater objects and measure distances. Seismic reflection methods send or detect waves that return from geological interfaces and are widely used to investigate subsurface structures. Medical ultrasound uses echoes from boundaries between tissues with different acoustic impedances to construct images.
The timing of a reflected signal can provide distance information when the propagation speed is known or estimated. In each case, the reflected wave contains information about the interaction between the incident wave and the environment, although interpretation must account for attenuation, scattering, geometry and the properties of the boundary.
Reflection can alter more than the direction of propagation. A reflected wave can acquire a phase shift depending on the boundary and wave type. For light reflecting from a medium with higher refractive index than the incident medium, the electric field can undergo a phase reversal of approximately 180 degrees under the conventional idealised conditions, whereas reflection from a lower refractive index medium does not produce the same reversal.
Phase changes upon reflection are important in thin film interference because waves reflected from different surfaces can therefore interfere constructively or destructively depending on both path difference and boundary phase changes. Similar phase effects occur for mechanical waves at boundaries with different impedances. Reflection is thus closely linked to interference and wave boundary conditions rather than being merely a geometric change in direction.
Reflection should be distinguished from scattering, refraction, diffraction and absorption. Reflection sends a wave back according to boundary conditions, while scattering redistributes wave energy because of particles, irregularities or structures. Refraction concerns transmitted propagation through a region with different wave speed, while diffraction concerns spreading and interference associated with spatial constraints. Absorption transfers wave energy into other forms, such as thermal energy, rather than returning it as a coherent reflected wave. Real boundaries commonly exhibit several of these processes simultaneously.
The practical behaviour depends on wavelength, incidence angle, surface structure, material composition, polarisation, frequency and geometry. Reflection is therefore best understood as a general wave interaction with a boundary, with simple laws such as equal incidence and reflection angles representing an important ideal case rather than a complete description of every real surface.
