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Specular reflection

Specular reflection, also known as regular reflection, is a type of reflection where light or other waves bounce off a smooth surface at a specific angle, producing a mirror-like image, in which the angle of incidence equals the angle of reflection relative to the surface normal.^[1]^[2] This phenomenon requires the reflecting surface to be microscopically smooth, with irregularities much smaller than the wavelength of the incident light (typically less than 1 micrometer for visible light in the 400–700 nanometer range), ensuring that incoming parallel rays remain parallel after reflection.^[3]^[2] In contrast to diffuse reflection, which scatters light in multiple directions from rough surfaces, specular reflection concentrates the reflected rays into a single direction, preserving the wavefront and enabling clear images in reflective optical systems like mirrors.^[1]^[3] The law of reflection, a fundamental principle in geometrical optics, governs this process and holds true regardless of the surface's orientation, as long as a local normal can be defined at the point of incidence.^[1]^[2] Specular reflection plays a crucial role in various applications, including the design of reflective optics, such as telescope mirrors, where it minimizes light loss and maintains image fidelity.^[2] It also explains everyday observations, like glare from wet roads during night driving or the sharp reflections in calm bodies of water, which can enhance visibility but also cause visual distractions.^[1] In advanced contexts, such as computer graphics and material science, models of specular reflection incorporate factors like surface curvature and material properties to simulate realistic lighting effects.^[2]

Definition and Principles

Core Definition

Specular reflection is the mirror-like reflection of waves, such as light, from a smooth surface, where the reflected wavefront remains planar and the angle of reflection equals the angle of incidence, resulting in a clear, undistorted image of the source.^[4] This phenomenon occurs when incoming waves bounce off the surface in a coherent, organized manner, maintaining the directionality of the original wavefront.^[5] Unlike scattering, specular reflection directs the energy into a single, predictable direction, enabling applications like mirrors and optical instruments.^[3] A key prerequisite for specular reflection is that the surface roughness must be much smaller than the wavelength of the incident waves, ensuring minimal disruption to the wavefront.^[3] For visible light, with wavelengths around 400–700 nm, this is achieved using highly polished surfaces such as optical flats, which maintain flatness to within a fraction of a wavelength, like λ/4 or better.^[6] Specular reflection applies not only to electromagnetic waves, including visible light and radio waves, but also to other wave types like sound waves on smooth boundaries and water waves on calm surfaces.^[1]^[7] The term "specular" originates from the Latin speculum, meaning "mirror," reflecting its association with polished, reflective surfaces.^[8] This concept was first systematically explored and described by the 11th-century polymath Alhazen (Ibn al-Haytham) in his seminal work Book of Optics, where he analyzed reflection principles through experimentation.^[9] In a basic ray diagram illustrating specular reflection, an incident ray approaches the surface at an angle θ to the normal (a line perpendicular to the surface at the point of incidence); the reflected ray then departs at the same angle θ on the opposite side of the normal, demonstrating the symmetry of the process.^[10] This geometric representation underscores the law of reflection, which governs the behavior and is explored in detail elsewhere.

Distinction from Diffuse Reflection

Diffuse reflection occurs when incident light waves are scattered in numerous directions due to microscopic surface irregularities on the scale of the light's wavelength, resulting in no formation of a distinct image, as seen in materials like matte paper.^[3] In contrast to specular reflection, which involves the coherent redirection of light rays from a smooth surface to produce a mirror-like image, diffuse reflection arises from multiple micro-reflections at varied angles on a rough surface, randomizing the outgoing light directions and disrupting wavefront coherence.^[1]^[11] The primary distinction between the two lies in surface microstructure: specular reflection preserves the phase relationships and spatial properties of the incident wavefront, enabling precise image formation, while diffuse reflection introduces random phase shifts through scattering, leading to a loss of directional specificity.^[12] Intermediate cases, such as glossy surfaces, exhibit a combination of both mechanisms, where a dominant specular component is broadened by moderate roughness, producing blurred highlights alongside scattered light.^[13] This duality allows for varied visual textures in materials like polished wood or painted plastics. The transition between specular and diffuse behavior is governed by the Rayleigh roughness criterion, which quantifies surface smoothness relative to the wavelength λ of the incident light. A surface produces predominantly specular reflection if the root-mean-square (RMS) roughness σ satisfies σ ≪ λ/8 (for normal incidence), ensuring phase differences between reflected rays remain below π/2 radians and constructive interference in the specular direction.^[14] Conversely, when σ ≈ λ, the phase variations exceed this threshold, causing destructive interference in the specular path and favoring diffuse scattering.^[14] Visually, specular reflection facilitates the creation of clear virtual images, as the organized ray paths mimic the original wavefront, while diffuse reflection yields uniform illumination across observers' views, minimizing glare and hotspots by distributing light evenly without concentrated reflections.^[3]^[1] This contrast underlies applications in optics, where specular surfaces are prized for imaging and diffuse ones for non-distracting lighting.

Law of Reflection

Geometric Formulation

In specular reflection, an incident light ray approaches a smooth reflecting surface and strikes it at a specific point of incidence. At this point, the surface normal is the line perpendicular to the tangent plane of the surface. The reflected ray then emanates from the same point, departing at an angle determined by the geometry of the interaction. This configuration forms the basis of the law of reflection, which governs the directional change of the light ray while preserving its specular nature.^[15] The angle of incidence, denoted as \theta_i, is defined as the angle between the direction of the incident ray and the surface normal. Similarly, the angle of reflection, \theta_r, is the angle between the direction of the reflected ray and the same normal. The law of reflection states that \theta_i = \theta_r, ensuring that the reflected ray mirrors the incident ray's approach relative to the normal. This equality holds for all points of incidence on an ideally smooth surface, directing the light coherently in a single outgoing direction.^[16] The incident ray, reflected ray, and surface normal all lie within a common plane called the plane of incidence. This planar confinement means that the reflection process occurs entirely within this two-dimensional plane, with no deviation out of plane for specular surfaces. As illustrated in the standard ray diagram, a horizontal reflecting surface is shown with a vertical normal at the incidence point, the incident ray approaching at \theta_i to the normal, and the reflected ray departing at \theta_r = \theta_i, all aligned in the plane of incidence.^[15] This geometric arrangement can be understood intuitively through the principles of wavefront continuity and energy conservation. Wavefront continuity requires that the phase of the electromagnetic wave remains matched across the reflecting interface, which is achieved only when the reflected wavefront propagates parallel to the incident one, enforcing equal angles. Energy conservation in the specular case directs the reflected energy into a focused beam along this path, avoiding dissipation that would occur with unequal angles or scattering.^[17]^[18]

Vector and Mathematical Formulation

The vector formulation of the law of reflection provides a quantitative means to compute the direction of the reflected ray, essential for simulations in optics and computer graphics. Assuming unit vectors for simplicity, the reflected direction \vec{R} is expressed as

\vec{R} = \vec{I} - 2 (\vec{I} \cdot \vec{N}) \vec{N},

where \vec{I} is the unit vector pointing in the direction of the incident ray (towards the reflecting surface), \vec{N} is the unit normal vector to the surface at the point of incidence, and \cdot denotes the dot product.^[19] This equation arises from vector algebra and applies to three-dimensional space, with the prerequisite of familiarity with dot products and vector projections.^[19] The derivation begins by decomposing the incident vector \vec{I} into its components parallel and perpendicular to the normal \vec{N}. The parallel (normal) component is the projection (\vec{I} \cdot \vec{N}) \vec{N}, and the perpendicular (tangential) component is \vec{I} - (\vec{I} \cdot \vec{N}) \vec{N}. Upon reflection, the tangential component remains unchanged, while the normal component reverses direction, equivalent to subtracting twice the projection from \vec{I}, yielding the formula above.^[20] This geometric reversal ensures the reflected ray lies in the plane of incidence and adheres to the kinematic principles of reflection.^[20] To verify that this formula satisfies the core law of reflection—equality of incident and reflected angles with the normal—consider the cosines of these angles. With the convention that \vec{I} points toward the surface, the incident angle \theta_i satisfies \cos \theta_i = -\vec{I} \cdot \vec{N} (negative due to the acute angle convention). For the reflected ray,

\vec{R} \cdot \vec{N} = [\vec{I} - 2 (\vec{I} \cdot \vec{N}) \vec{N}] \cdot \vec{N} = \vec{I} \cdot \vec{N} - 2 (\vec{I} \cdot \vec{N}) (\vec{N} \cdot \vec{N}) = \vec{I} \cdot \vec{N} - 2 (\vec{I} \cdot \vec{N}) = - \vec{I} \cdot \vec{N},

since |\vec{N}| = 1. Thus, \cos \theta_r = \vec{R} \cdot \vec{N} = \cos \theta_i, confirming \theta_r = \theta_i.^[19]^[20] In computational contexts like ray tracing, this vector equation enables efficient calculation of reflection paths for rendering realistic scenes. It forms the basis for specular shading in models such as the Phong illumination model, where \vec{R} determines the intensity of highlights by its alignment with the viewer direction, extending the pure directional law to account for material glossiness.

Reflectivity

Fundamental Concepts

Reflectivity, often denoted as ρ or reflectance, is defined as the ratio of the power of electromagnetic radiation reflected by a surface to the power of the incident radiation, resulting in a dimensionless quantity bounded between 0 and 1.^[21] In the context of specular reflection, this coefficient specifically quantifies the mirror-like component of the reflected energy, where light is redirected coherently according to the law of reflection.^[22] For ideal perfect reflectors, ρ approaches 1, indicating nearly complete reflection without loss, while ρ = 0 corresponds to total absorption or transmission. Reflectivity can be categorized into types such as normal incidence reflectivity, which measures the reflection at perpendicular incidence, and distinctions between total reflectance (encompassing all reflected light) and specular reflectance (the portion directed specularly, excluding diffuse scattering).^[23] For non-scattering surfaces, energy conservation dictates that the sum of reflectivity ρ, absorptance α (the fraction absorbed), and transmittance τ (the fraction transmitted) equals 1, ensuring no net energy loss or gain at the interface.^[24] Reflectivity is typically measured using spectrophotometers, which illuminate the surface with monochromatic light and detect the reflected intensity to determine wavelength-dependent values ρ(λ), providing spectral profiles across ranges like the visible spectrum.^[25] For example, polished silver exhibits a high normal incidence reflectivity of approximately 0.98 in the visible light range, making it a benchmark for efficient specular mirrors.^[26] Kirchhoff's law of thermal radiation, applicable at thermal equilibrium, states that for opaque bodies (where τ = 0), the emissivity ε equals the absorptance α, which in turn equals 1 - ρ, linking reflective properties to thermal emission behavior.^[27] This principle underscores the reciprocity between absorption and emission for surfaces in thermodynamic balance.^[28]

Angular and Material Dependence

The reflectivity in specular reflection exhibits significant dependence on both the angle of incidence and the optical properties of the materials involved at the interface. For light transitioning between two media with refractive indices n_1 and n_2, the Fresnel equations provide the precise amplitude reflection coefficients, which squared yield the power reflectivity \rho. These equations account for the polarization state of the light and the resulting transmitted angle \theta_t via Snell's law, n_1 \sin \theta_i = n_2 \sin \theta_t.^[29] For unpolarized light at oblique incidence, the perpendicular (s-polarized) reflectivity is given by

\rho_s = \left( \frac{n_1 \cos \theta_i - n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t} \right)^2,

while the parallel (p-polarized) reflectivity is

\rho_p = \left( \frac{n_1 \cos \theta_t - n_2 \cos \theta_i}{n_1 \cos \theta_t + n_2 \cos \theta_i} \right)^2.

The overall reflectivity for unpolarized light is then the average, \rho = (\rho_s + \rho_p)/2. These expressions predict that reflectivity generally increases with the angle of incidence, approaching unity at grazing angles for dielectrics, while remaining relatively constant for metals.^[29]^[30] At normal incidence (\theta_i = 0), the Fresnel equations simplify to a single form independent of polarization:

\rho = \left( \frac{n_1 - n_2}{n_1 + n_2} \right)^2.

This yields low reflectivity for common dielectric interfaces, such as air-glass (n_1 \approx 1, n_2 \approx 1.5), where \rho \approx 0.04 across visible wavelengths, explaining the partial transparency of glass.^[29]^[31] Material properties profoundly influence this angular behavior through the refractive index n, which itself varies with wavelength. Dielectrics exhibit low normal-incidence reflectivity that rises sharply toward grazing angles due to the geometric mismatch in wave vectors at the interface. In contrast, metals maintain high, nearly angle-independent reflectivity—often exceeding 90%—owing to their free electrons, which enable strong collective oscillations that efficiently reflect incident electromagnetic waves across a broad angular range. Wavelength dependence further modulates these effects; for instance, metallic reflectivity decreases at longer infrared wavelengths but remains dominant in the visible spectrum.^[30]^[32]/Optical_Properties/Metallic_Reflection) The Fresnel equations derive from the boundary conditions imposed by Maxwell's equations on the tangential components of the electric and magnetic fields at the interface between two isotropic, homogeneous media, ensuring continuity of the fields and their derivatives. These assumptions hold well for smooth, non-absorbing interfaces but overlook surface roughness, which scatters light diffusely, and detailed absorption mechanisms, such as those in conducting media where complex refractive indices are required for full accuracy.^[33]^[29]

Optical Consequences

Total Internal Reflection

Total internal reflection (TIR) is a phenomenon that occurs when light propagating in a medium with a higher refractive index (n₁ > n₂) encounters an interface with a medium of lower refractive index at an incidence angle θ_i greater than the critical angle θ_c, resulting in complete reflection of the incident power back into the denser medium with no transmission across the boundary (ρ = 1).^[34] This condition arises from the principles of specular reflection, where the reflected ray follows the law of reflection, but the absence of a transmitted ray distinguishes TIR from partial reflection at subcritical angles. The critical angle is defined as θ_c = arcsin(n₂/n₁), ensuring that all energy is specularly reflected for θ_i > θ_c.^[35] The foundation of TIR lies in Snell's law, which relates the angles of incidence and transmission at the interface: n₁ sin θ_i = n₂ sin θ_t. At the critical angle, the transmitted angle θ_t reaches 90°, grazing the interface, such that sin θ_c = n₂/n₁, and for larger θ_i, no real θ_t exists, leading to total reflection.^[34] This derivation highlights how the refractive index contrast enforces the boundary condition, preventing propagation into the rarer medium. Historically, the underlying principles of refraction and internal reflection were described in the 17th century by Willebrord Snell in 1621 and independently by René Descartes in 1637, who formalized the law that enables the prediction of TIR.^[36] During TIR, although no power transmits, a non-propagating evanescent wave forms in the rarer medium, decaying exponentially away from the interface over a distance of typically a few wavelengths, which allows for interactions like absorption in attenuated total reflection spectroscopy.^[37] Additionally, the reflected beam experiences a lateral displacement known as the Goos-Hänchen shift, arising from a phase shift upon reflection that effectively penetrates the interface slightly before returning, with the shift magnitude depending on the incidence angle and wavelength.^[38] This shift, first observed experimentally in 1947, provides a measurable consequence of the evanescent field's influence on the reflection process.^[38]

Polarization Effects

When unpolarized light undergoes specular reflection at an interface between two media, the reflected light becomes partially polarized, with the s-polarized component (electric field perpendicular to the plane of incidence) reflecting more strongly than the p-polarized component (electric field parallel to the plane of incidence).^[39] This preferential reflection arises from the angular dependence of the Fresnel reflection coefficients, which favor s-polarization at most incidence angles.^[40] A special case occurs at Brewster's angle, \theta_B = \arctan\left(\frac{n_2}{n_1}\right), where n_1 and n_2 are the refractive indices of the incident and transmitting media, respectively, and the p-polarized reflectivity \rho_p vanishes completely.^[31] At this angle, the reflected light is entirely s-polarized, while the transmitted light is fully p-polarized.^[39] This phenomenon derives from the Fresnel equations: \rho_p = 0 when the incident angle \theta_i and transmitted angle \theta_t are complementary, satisfying \theta_i + \theta_t = 90^\circ, as the dipole radiation from induced oscillations in the material cancels in the reflection direction for p-polarization.^[39] In configurations involving multiple reflections, such as a stack of parallel glass plates oriented at Brewster's angle (known as a pile-of-plates polarizer), successive reflections progressively enhance s-polarization in the reflected beam while transmitting predominantly p-polarized light, achieving high degrees of linear polarization.^[40] Phase differences between s- and p-components across these reflections can further result in elliptical polarization for certain incident states. From a quantum perspective, the absence of p-polarized reflection at Brewster's angle stems from the fact that induced dipole oscillations in the material, driven by the incident field, do not radiate perpendicularly to their axis, suppressing emission in the reflection direction for dipoles aligned with p-polarization.^[41]

Image Formation

In specular reflection from a plane mirror, the image formed is virtual, erect, and the same size as the object, with the image distance behind the mirror equal to the object distance in front.^[42] This virtual image appears at the symmetric position relative to the mirror surface, resulting from the extension of reflected rays backward.^[43] Additionally, the image exhibits lateral inversion, where left and right are reversed compared to the object.^[42] For curved mirrors, the nature of the image depends on whether the mirror is concave or convex and the object's position relative to the focal point. In a concave mirror, which converges light, real and inverted images form when the object is placed beyond the focal point, while virtual, erect, and magnified images occur when the object is within the focal length.^[44] The focal length f is half the radius of curvature R, given by f = \frac{R}{2}, with f positive for concave mirrors.^[44] Convex mirrors, which diverge light, always produce virtual, erect, and diminished images regardless of object position, with f negative.^[44] Image location and magnification for both types are determined by the mirror equation:

\frac{1}{f} = \frac{1}{o} + \frac{1}{i}

where o is the object distance and i is the image distance (positive for real images in concave mirrors, negative for virtual).^[45] Image formation in curved mirrors relies on the paraxial approximation, which assumes small angles relative to the optical axis for accurate predictions using the mirror equation.^[46] Ray tracing under this approximation uses three principal rays from the object tip: (1) a ray parallel to the principal axis, which reflects through the focal point; (2) a ray passing through the focal point before reflection, which emerges parallel to the axis; and (3) a chief ray directed toward the mirror's center of curvature, which reflects back along the same path.^[47] The intersection of these reflected rays (or their backward extensions for virtual images) locates the image. Aberrations limit the quality of images in spherical mirrors. Spherical aberration occurs because paraxial rays focus at a different point than marginal rays, with outer zones of the mirror focusing closer to the surface in concave mirrors, blurring the image.^[43] Chromatic aberration is absent in ideal mirrors since reflection does not disperse wavelengths, though slight effects may arise from wavelength-dependent reflectivity of mirror coatings.^[48] These aberrations, particularly spherical, can be corrected using aspheric mirrors, which deviate from spherical curvature to ensure all zones focus at the same point.^[43] Specular reflection preserves the geometric arrangement of rays, enabling stereopsis and depth perception in virtual images as the binocular disparity matches that of the apparent object position behind the mirror.^[49]

Applications and Examples

Everyday Phenomena

Specular reflection is commonly observed in natural settings where smooth surfaces create mirror-like images. Calm water surfaces, such as those on a still lake or pond, act as horizontal mirrors, reflecting the sky, surrounding landscape, and nearby objects with high fidelity due to the flat interface between air and water.^[50] Similarly, wet roads after rain exhibit specular reflection by forming a thin, smooth layer of water that mirrors oncoming headlights, creating bright glares that can dazzle drivers and reduce visibility at night.^[51] Dew on leaves in the morning often produces small specular glints, as the curved droplets on smooth leaf surfaces reflect sunlight sharply, contributing to the sparkling appearance of foliage. In household environments, specular reflection plays a practical role in daily routines. Plane mirrors used for grooming, such as those in bathrooms, provide clear virtual images of the face and body by reflecting light rays at equal angles to the incident rays from smooth silvered glass surfaces.^[52] Polished metal utensils, like stainless steel spoons or knives, demonstrate specular properties when clean and buffed, reflecting tabletop objects or light sources distinctly to aid in tasks like checking appearance or signaling. Glass windows in homes partially reflect incoming light specularly while transmitting the rest, often creating faint mirror images of indoor scenes superimposed on the outdoor view, especially at oblique angles.^[50] Atmospheric conditions can bend light paths to produce specular-like effects through refraction rather than direct reflection. Mirages over hot roads or deserts arise from temperature gradients in the air layers near the ground, where cooler air above warmer air acts like a curved refractive medium, creating inverted, elongated images that mimic specular reflections from an illusory water surface.^[53] Certain animal adaptations leverage specular or related reflective mechanisms for survival and display. Iridescent feathers in birds, such as those of hummingbirds or peacocks, produce angle-dependent specular-like reflections through nanostructured barbules that interfere with light, generating shifting colors visible during flight or courtship to attract mates or deter rivals.^[54] In cats, the tapetum lucidum—a reflective layer behind the retina—enhances low-light vision by retroreflecting unabsorbed light back through the photoreceptors, briefly producing a specular glow in their eyes when illuminated at night.^[55] Seasonally, specular reflection becomes prominent in winter landscapes. Ice rinks, with their highly polished frozen surfaces, reflect arena lights and surroundings sharply, creating gliding mirror effects that enhance the visual appeal for skaters and spectators. Frost patterns on windows or ground, forming smooth crystalline layers overnight, exhibit specular glints under sunlight, sparkling as the ice facets mirror the environment before sublimating.^[50]

Scientific and Technological Uses

Specular reflection forms the foundation of numerous optical instruments designed to manipulate light for imaging and measurement. In reflecting telescopes, parabolic mirrors exploit the precise angular dependence of specular reflection to focus parallel incoming rays from distant objects to a single focal point, minimizing aberrations and enabling high-resolution astronomical observations. Similarly, specialized reflective microscope objectives incorporate mirrors with coatings to achieve chromatic aberration-free imaging across broad spectral ranges, where specular reflection from curved mirrors directs light efficiently without dispersion.^[56] Periscopes utilize prisms that leverage total internal reflection—a form of specular reflection at the glass-air interface—to redirect light paths by 90 degrees, allowing visibility around obstacles in applications such as submarines and vehicles without the need for external mirrors. In laser systems and fiber optics, specular reflection is engineered for efficient light confinement and amplification. Dielectric mirrors, consisting of multilayer thin-film stacks, achieve reflectivities exceeding 99.9% through constructive interference of specularly reflected waves at specific wavelengths, serving as essential components in laser resonators to sustain optical feedback. Optical fibers guide light over long distances by relying on total internal reflection at the core-cladding interface, where specular reflection ensures minimal loss and preserves signal integrity for telecommunications and sensing. Advanced coatings further tailor specular reflection for performance optimization. Anti-reflective layers, typically quarter-wave dielectric films, reduce surface reflectivity to below 1% via destructive interference of reflected rays, enhancing transmission in lenses and solar cells. Conversely, high-reflectivity coatings on solar sails maximize specular reflection of sunlight to generate thrust through photon momentum transfer, with aluminum or dielectric layers achieving near-unity reflectance in the visible spectrum for propulsion in space missions. Although primarily optical, specular reflection principles extend briefly to acoustics, where smooth surfaces in sonar systems produce mirror-like echoes for underwater mapping and target detection, analogous to optical specular returns. Contemporary advancements include metamaterials and metasurfaces that enable precise control of specular reflection. These engineered structures manipulate phase and amplitude to achieve perfect anomalous reflection or suppress specular components, facilitating applications in beam steering and stealth technologies. In LIDAR systems for environmental mapping, specular reflections from smooth surfaces provide strong returns for accurate distance measurement and 3D reconstruction, though multibounce effects require specialized algorithms for interpretation.

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[PDF] 5. Plane Electromagnetic Waves ( ) ( ) ) - Galileo and Einstein
But an oscillating dipole, as we shall learn, emits zero radiation along its axis. This angle is called Brewster's angle. For unpolarized incident radiation ...Missing: explanation | Show results with:explanation
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[PDF] Chapter 23 The Reflection of Light: Mirrors
The Formation of Images by a Plane Mirror. Your image in a flat mirror has four properties: 1. It is upright. 2. It is the same size as you are. 3. The image ...Missing: erect | Show results with:erect<|control11|><|separator|>
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Physics of Light and Color - Introduction to Mirrors
Nov 13, 2015 · Finally, when the object rests against the surface of the mirror, the virtual image once again becomes the same size as the object.
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Mirrors
The focal length f and the radius of curvature R = 2f are positive for a concave mirror and negative for a convex mirror. For a concave mirror the reflecting ...
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Images Formed by Curved Mirrors
The object distance do, the image distance di, and the mirror's focal length f are related by the image equation, Further examples: Consider an object placed ...
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Mirrors
Mirrors can form images. In the paraxial approximation we can derive the mirror equation for convex and concave spherical mirrors using the law of reflection.Missing: chief | Show results with:chief
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Ray Diagrams for Mirrors - HyperPhysics
Mirror ray tracing uses rays parallel to the optic axis, through the focal point, and through the center of curvature. Back-projecting rays helps construct the ...
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18.7 Aberration
A: Mirrors do not have chromatic aberration. A mirrors has only a single surface to grind instead of two for a lens. Mirrors can also be supported from the back ...
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Perception Lecture Notes: Depth, Size, and Shape
Stereopsis: greek for "solid sight". Close one eye, and hold up your two index fingers, one fairly close to your face and one as far as you can reach.Missing: specular reflection
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Light and Color - Reflection of Light - Molecular Expressions
Nov 13, 2015 · Perhaps the best example of specular reflection, which we encounter on a daily basis, is the mirror image produced by a household mirror that ...
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Demos: 7A-02 Specular and Diffuse Reflection - Purdue Physics
But when it is wet it becomes a mirror-like surface and most of the light is reflected forward. Also the oncoming headlights are directly reflected into your ...
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On the Observation of Unresolved Surface Features of a Planet
... leaves as the antisolar point is approached. A stubble field is a uniquely ... Such specular reflection may identify dew drops, however. 2 The diffuse ...
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Light and Color - Specular and Diffuse Reflection: Interactive Tutorial
Sep 10, 2018 · Perhaps the best example of specular reflection, which we encounter on a daily basis, is the mirror image produced by a household mirror that ...
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[PDF] Road surface mirage: A bunch of hot air?
However, it was also suggested that the mirage is just a phenomenon of specular reflection ... rior mirage phenomenon caused by the temperature gradient.
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Nanostructural basis of rainbow-like iridescence in common ...
Angle- resolved specular reflectance of the green region of the feather is shown in Fig. 3, with the incident angle ranging from 10 ° to 45° by 5 ...
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Feline Vision Problems: A Host of Possible Causes
Cats also have a specialized layer of tissue beneath the retina that reflects incoming light. This structure—the tapetum lucidum—reflects light not absorbed by ...