Reflection (Optics)

Reflection is the return of light into the medium from which it arrived after encountering a surface or an interface between materials. In optics, it explains mirror images, glints on smooth surfaces, and much of the light scattered back from ordinary objects. Reflection may occur together with transmission and refraction; a transparent surface can therefore reflect some incident light while allowing the remainder to pass through. Its direction, intensity, and polarization depend on the interface and the properties of the adjoining media. (openstax.org)

Law of reflection

For specular reflection at an ordinary smooth interface, the incident ray, reflected ray, and surface normal lie in one plane. The normal is perpendicular to the surface at the point of incidence. The law of reflection states

where both angles are measured from the normal, not from the surface. At normal incidence, the reflected ray retraces the incident path. On a curved surface, the law applies using the local normal at each point. These rules form a foundation of geometrical optics and the construction of ray diagrams. (openstax.org)

Repeated reflections can produce more specialized behavior. A retroreflector returns light approximately toward its source over a range of incident directions. A corner-cube reflector accomplishes this with three mutually perpendicular reflecting surfaces: successive reflections reverse all three components of the ray’s direction. This differs from a single plane mirror, which returns a ray along its incoming path only at normal incidence. (openstax.org)

Specular and diffuse reflection

Specular reflection occurs when a surface is sufficiently smooth relative to the light’s wavelength. Parallel incident rays then remain parallel after reflection from a plane surface, permitting a recognizable image. Polished mirrors and calm water surfaces provide familiar examples. (openstax.org)

Diffuse reflection distributes reflected light among many directions. A rough surface presents differently oriented local normals, so neighboring portions redirect incident light differently. The local law of reflection is not violated; rather, the aggregate reflection lacks a single direction. Paper is visible from many viewpoints because it scatters light instead of producing a sharp mirror image. Many real surfaces have both specular and diffuse components, so these categories describe limiting behaviors rather than mutually exclusive material types. (openstax.org)

Electromagnetic description and reflectance

In wave optics, reflection follows from Maxwell’s equations and the boundary conditions imposed on electromagnetic fields at an interface. The Fresnel equations describe reflected and transmitted amplitudes for ideal plane waves. They distinguish between amplitude reflection coefficients and reflectance, the fraction of incident optical power reflected. Reflectance depends on incidence angle, wavelength, polarization, and the materials’ optical properties. (ocw.mit.edu)

At normal incidence between transparent, nonmagnetic media with real refractive indices $n_1$ and $n_2$,

For example, taking $n_1=1.0$ for air and $n_2=1.5$ for glass gives $R=0.04$: approximately four percent of incident power is reflected at one uncoated interface. This is an illustrative calculation, not a universal reflectance for glass. (ocw.mit.edu)

Reflection also changes wave phase. At normal incidence, reflection from a lower-index medium toward a higher-index transparent medium reverses the reflected electric field’s phase by $\pi$; the reverse index ordering does not. Phase relationships become important when reflected waves combine through interference. (ocw.mit.edu)

Polarization and total internal reflection

At oblique incidence, the electric field is resolved into an s component, perpendicular to the plane of incidence, and a p component, parallel to it. Their reflection coefficients generally differ. For an interface between transparent, nonmagnetic media, the p-polarized reflection vanishes at Brewster’s angle, defined by

Consequently, reflection of initially unpolarized light at this angle produces s-polarized reflected light. Polarizing filters exploit this directional preference to suppress glare from water or glass. (ocw.mit.edu)

Total internal reflection occurs when light travels toward a lower-index medium and strikes the interface above the critical angle:

In the ideal lossless case, all incident power is reflected. Nevertheless, an evanescent field extends into the lower-index medium and decays away from the interface; total reflection does not imply that the field is absent there. This mechanism confines light in optical fibers and other optical waveguides. (openstax.org)

Mirrors, coatings, and image formation

A mirror combines a reflecting surface with a geometry that controls ray directions. A plane mirror forms an upright virtual image of the same size as the object, at an equal distance behind the mirror. Concave mirrors can form real or virtual images depending on object position; convex mirrors produce diminished, upright virtual images of real objects. For spherical mirrors, the paraxial approximation gives a focal length equal to half the radius of curvature. Departures from this approximation produce spherical aberration. (openstax.org)

Metallic coatings commonly use aluminum, silver, or gold, with different spectral performance. Precision instruments often employ first-surface mirrors, avoiding passage through a glass substrate before reflection and reducing unwanted ghost images. A dielectric mirror instead uses alternating layers of different refractive index, arranged so that partial reflections reinforce one another. Such coatings can provide very high reflectance within selected wavelength ranges. (edmundoptics.com)

These principles serve different optical functions. A reflecting telescope uses curved mirrors to collect light and form images. In a laser, mirrors form an optical resonator, with coating reflectance controlling how much light remains in the cavity or exits through an output mirror. (openstax.org)