Specular reflection
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Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.[1]
The law of reflection states that a reflected
Specular reflection may be contrasted with diffuse reflection, in which light is scattered away from the surface in a range of directions.
Law of reflection
When light encounters a boundary of a material, it is affected by the optical and electronic response functions of the material to electromagnetic waves. Optical processes, which comprise
Reflection may occur as specular, or mirror-like, reflection and
Light propagates in space as a wave front of electromagnetic fields. A ray of light is characterized by the direction normal to the wave front (wave normal). When a ray encounters a surface, the angle that the wave normal makes with respect to the
The law of reflection states that the angle of reflection of a ray equals the angle of incidence, and that the incident direction, the surface normal, and the reflected direction are
When the light impinges perpendicularly to the surface, it is reflected straight back in the source direction.
The phenomenon of reflection arises from the diffraction of a plane wave on a flat boundary. When the boundary size is much larger than the wavelength, then the electromagnetic fields at the boundary are oscillating exactly in phase only for the specular direction.
Vector formulation
The law of reflection can also be equivalently expressed using
where is a scalar obtained with the dot product. Different authors may define the incident and reflection directions with different signs. Assuming these
where is the so-called
in terms of the identity matrix and twice the outer product of .
Reflectivity
Measurement of specular reflection is performed with normal or varying incidence reflection spectrophotometers (reflectometer) using a scanning variable-wavelength light source. Lower quality measurements using a
Consequences
Internal reflection
When light is propagating in a material and strikes an interface with a material of lower
Polarization
When light strikes an interface between two materials, the reflected light is generally partially polarized. However, if the light strikes the interface at Brewster's angle, the reflected light is completely linearly polarized parallel to the interface. Brewster's angle is given by
Reflected images
The image in a flat mirror has these features:
- It is the same distance behind the mirror as the object is in front.
- It is the same size as the object.
- It is the right way up (erect).
- It is reversed.
- It is virtual, meaning that the image appears to be behind the mirror, and cannot be projected onto a screen.
The reversal of images by a plane mirror is perceived differently depending on the circumstances. In many cases, the image in a mirror appears to be reversed from left to right. If a flat mirror is mounted on the ceiling it can appear to reverse up and down if a person stands under it and looks up at it. Similarly a car turning left will still appear to be turning left in the rear view mirror for the driver of a car in front of it. The reversal of directions, or lack thereof, depends on how the directions are defined. More specifically a mirror changes the handedness of the coordinate system, one axis of the coordinate system appears to be reversed, and the chirality of the image may change. For example, the image of a right shoe will look like a left shoe.
Examples
A classic example of specular reflection is a mirror, which is specifically designed for specular reflection.
In addition to
Non-electromagnetic waves can also exhibit specular reflection, as in
See also
- Geometric optics
- Hamiltonian optics
- Reflection coefficient
- Reflection (mathematics)
- Specular highlight
- Specularity
Notes
- S2CID 5058976
- ISBN 978-0-486-24074-9.
- ISBN 978-1-351-40468-6.
- ISBN 978-0-486-17347-4.
- ISBN 978-3-662-07032-1.
- ^ Selin 2008, p. 1817.
- ISBN 978-0-486-17347-4.
- ISBN 978-0-19-957336-3.
- S2CID 238899623.
- ISBN 978-1-85233-902-9. Archivedfrom the original on 2018-01-14.
- ISBN 978-1-56881-234-2. Archived from the original on 2010-03-07. Practical linear algebra: a geometry toolbox at Google Books
- ^ Hecht 1987, p. 100.
References
- Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. ISBN 0-201-11609-X.