Reflection is the process in which a wave encounters a boundary or discontinuity and returns, wholly or partially, into the region from which it originated. For specular reflection from a smooth surface, the angle of reflection equals the angle of incidence, with both angles measured relative to the normal at the point of incidence.
This geometrical rule applies to electromagnetic waves such as visible light and radio waves, as well as mechanical waves such as sound, provided the relevant surface or interface is sufficiently smooth relative to the wavelength. Reflection does not require a perfectly rigid or perfectly conducting boundary; real interfaces generally divide incident energy among reflected, transmitted, absorbed and sometimes scattered components.
In optics, reflection is governed by the electromagnetic properties of the interface, including refractive index, electrical conductivity and magnetic response. The Fresnel equations describe the amplitude and phase of reflected and transmitted electromagnetic waves for an interface between two media and show that reflection depends on polarisation and angle of incidence. At normal incidence between non-magnetic materials, the reflectance can be expressed in terms of the refractive indices as \(R=((n_1-n_2)/(n_1+n_2))^2\) for idealised lossless media. Metals can reflect strongly because their mobile electrons interact with the incident electromagnetic field, while dielectrics can range from weakly to strongly reflective depending on their optical properties.
Reflection may be specular or diffuse. A polished mirror produces predominantly specular reflection because its surface variations are small compared with the wavelength of visible light, preserving a well-defined relationship between incident and reflected directions. A rough wall produces diffuse reflection because microscopic surface variations redirect incident energy over a range of angles. The same distinction applies to sound: a large smooth hard wall can create a strong acoustic reflection, whereas a rough, irregular or absorptive surface can scatter and dissipate acoustic energy. Whether a surface behaves as smooth therefore depends partly on wavelength, meaning that a surface can appear smooth to one type of wave and rough to another.
Reflection is central to image formation. A plane mirror forms a virtual image with geometric properties determined by the law of reflection, while curved mirrors can form real or virtual images depending on their geometry and the location of the object. Concave mirrors can converge approximately parallel rays towards a focus, which is useful in telescopes, searchlights and optical instruments. Convex mirrors provide a wider field of view and form reduced virtual images, making them useful for surveillance and vehicle mirrors. More advanced reflective systems use multilayer coatings, metallic films, dielectric stacks and engineered surfaces to control reflectivity over selected wavelength ranges.
Acoustic reflection is responsible for echoes, reverberation and many practical sensing techniques. An echo occurs when a reflected sound arrives sufficiently separated in time from the direct sound to be perceived as a distinct repetition, whereas reverberation consists of many overlapping reflections that persist after the source stops. The time delay of a reflected pulse can be used to estimate distance when the wave speed is known, forming the basis of sonar and related ranging methods. Architectural acoustics therefore considers reflection carefully because useful reflections can reinforce sound and improve coverage, while poorly controlled reflections can produce echoes, flutter echoes, comb filtering and reduced speech intelligibility.
Reflection also occurs at interfaces where waves encounter changes in mechanical impedance. For a sound wave travelling through air towards a solid surface, the large mismatch in acoustic impedance generally produces substantial reflection. In strings, ropes and transmission lines, whether a reflected pulse returns inverted or non-inverted depends on the boundary conditions and the relative impedance of the termination. Electrical transmission lines exhibit analogous reflection when their characteristic impedance does not match the load impedance. The voltage and current behaviour of these reflected signals is important in radio-frequency engineering, high-speed digital systems and telecommunications.
Reflection is distinct from absorption, transmission and scattering, although these processes commonly occur together. Absorption converts part of the wave's energy into other forms, such as heat, while transmission carries energy through the boundary or material. Scattering redirects energy because of irregularities, particles or structures, often producing a range of propagation directions. A real surface can therefore have a measurable reflectance, transmittance, absorptance and scattering behaviour, with the relative proportions depending on wavelength, angle, polarisation, material properties and surface structure. Energy conservation provides an important constraint, although losses and interactions with the medium must be included in a complete treatment.
Modern technologies exploit controlled reflection rather than merely trying to eliminate it. Radar systems use reflected radio waves to detect and locate objects, while lidar uses reflected laser light for ranging and environmental measurement. Reflective coatings can be designed to reject infrared radiation, preserve visible reflectance or selectively enhance particular wavelengths. Antennas and waveguides use conducting boundaries to guide electromagnetic fields through controlled reflections, and microwave cavities use reflections to establish resonant field patterns. Reflection is therefore both a fundamental boundary phenomenon and an engineering resource whose behaviour can be manipulated through geometry, material selection, impedance matching, surface structure and frequency.
