Hubbry Logo
CatoptricsCatoptricsMain
Open search
Catoptrics
Community hub
Catoptrics
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Catoptrics
Catoptrics
Catoptrics
View on Wikipedia
from Wikipedia

Light path of a Newtonian (catoptric) telescope

Catoptrics (from Ancient Greek: κατοπτρικός katoptrikós, "specular",[1] from Ancient Greek: κάτοπτρον katoptron "mirror")[2] deals with the phenomena of reflected light and image-forming optical systems using mirrors. A catoptric system is also called a catopter (catoptre).

History

[edit]

Ancient Texts

[edit]

Catoptrics is the title of two texts from ancient Greece:

  • Catoptrics written by "Pseudo-Euclid"; although the book is attributed to Euclid,[3] its contents are a combination of knowledge dating from Euclid's time together with information which dates to the later Roman period.[4] It has been argued that the book may have been compiled by the 4th century mathematician Theon of Alexandria.[4] The book covers the mathematical theory of mirrors, particularly the images formed by plane and spherical concave mirrors.
  • Catoptrics written by Hero of Alexandria, this work concerns the practical application of mirrors for visual effects. In the Middle Ages, this work was falsely ascribed to Ptolemy. It only survives in a Latin translation.[5]

The Latin translation of Alhazen's (Ibn al-Haytham) main work, Book of Optics (Kitab al-Manazir),[6] exerted a great influence on Western science: for example, on the work of Roger Bacon, who cites him by name.[7] His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the problem known as "Alhazen's problem".[8] Alhazen's work influenced Averroes' writings on optics,[citation needed] and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (d. c. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).[9][10]

Renaissance

[edit]

16th century Jewish-Ferraresi physicist Rafael Mirami wrote a treatise on the subject, Compendiosa introduttione alla prima parte della specularia, which became influential in a revival of the field, and contributed towards astronomical calculations instigated by Pope Gregory XIII, that led to the creation of the Gregorian Calendar.[11][12]

Catoptric telescopes

[edit]

The first practical catoptric telescope (the "Newtonian reflector") was built by Isaac Newton as a solution to the problem of chromatic aberration exhibited in telescopes using lenses as objectives (dioptric telescopes).

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Catoptrics

View on Grokipedia
from Grokipedia
Catoptrics is the branch of optics that studies the reflection of light rays from surfaces, particularly mirrors, and the resulting visual appearances and image formation. The term originates from the Greek katoptron, meaning "mirror," combining kata ("against" or "down") and optos ("seen" or "visible"), reflecting its focus on reflective phenomena. Distinct from dioptrics, which examines refraction through transparent media, catoptrics emphasizes geometric principles governing how light bounces off opaque surfaces to produce images, often employing the law of reflection where the angle of incidence equals the angle of reflection. The foundational text on catoptrics is Euclid's Catoptrics, composed around 300 BCE, which treats reflection geometrically and assumes travels in straight lines from the eye in a visual , enabling theorems on apparent sizes and positions of reflected objects. Euclid's work established core propositions, such as the equality of incident and reflected angles, building on earlier intuitive understandings of mirrors in ancient cultures. Subsequent advancements came from in the 1st century CE, who in his Catoptrics derived the reflection using a shortest-path and explored infinite speed, while also addressing localization via the " rule." By the CE, Claudius Ptolemy expanded catoptrics in his , empirically verifying reflection laws and analyzing images in plane, convex, and concave mirrors, including detailed ray-tracing for spherical surfaces. In the , (Alhazen, c. 965–1040 CE) revolutionized the field in Books IV and V of his Kitāb al-Manāẓir (), conducting experiments to confirm reflection principles and solving complex problems like —involving rays from two points reflecting off a spherical mirror to meet at a specific point. These developments laid the groundwork for later optical instruments, such as burning mirrors studied by Diocles (late 2nd century BCE), who proved parabolic mirrors focus sunlight to a point. Catoptrics thus evolved from ancient geometric theory to a cornerstone of optical science, influencing applications in telescopes and modern mirror-based systems.

Fundamentals of Reflection

Definition and Scope

Catoptrics is the branch of that exclusively studies the reflection of from mirrors and other specular surfaces, focusing on the formation of images through such reflections. The term derives from word katoptron, meaning "mirror," which combines kata (against or down) and optos (seen or visible), reflecting its origins in ancient inquiries into mirrored vision. The scope of catoptrics encompasses , where light rays from smooth surfaces like polished metals or glass mirrors bounce off at predictable angles, enabling clear , in contrast to from rough surfaces, which scatters light in multiple directions without forming distinct images. It deliberately excludes phenomena involving , as studied in , and wave-based effects like , concentrating instead on geometric principles of ray tracing. Within broader , catoptrics forms one foundational pillar alongside these other branches, providing essential tools for understanding reflective optical systems. Originating in scholarship, catoptrics laid early groundwork for systematic optical analysis, with detailed historical developments explored elsewhere. Central to its study are key concepts such as the incident ray (the incoming light path), the reflected ray (the outgoing light path), the normal line (a at the point of reflection), the angle of incidence (between the incident ray and normal), and the angle of reflection (between the reflected ray and normal). These elements underpin all catoptric investigations, emphasizing the precise geometry of light paths on reflective interfaces.

Basic Properties of Reflected Light

Upon reflection, light wavefronts behave according to Huygens' principle, which posits that every point on an incident wavefront acts as a source of secondary spherical wavelets propagating forward at the , with the reflected wavefront forming as the envelope tangent to these wavelets. For a incident on a flat mirror, this results in a reflected that maintains parallelism, enabling the formation of virtual images behind the mirror surface. In catoptric systems, such wavefront propagation explains how coherent light sources produce focused real images in converging setups, though the principle applies universally to reflection phenomena. Reflection alters the polarization state of light, particularly for unpolarized incident beams interacting with or metallic surfaces. At —the incidence angle where the reflected ray is perpendicular to the refracted ray—the reflected light becomes fully polarized parallel to the reflecting surface (s-polarization), while the transmitted component retains partial polarization. This effect arises from the differential reflection coefficients for parallel (p-) and perpendicular (s-) polarizations, with metals exhibiting stronger polarization changes due to their conductive properties compared to s. Such polarization shifts are observable in everyday scenarios, like glare reduction on water surfaces, and underpin catoptric polarizers. The intensity of reflected light adheres to , where the sum of reflected and transmitted intensities equals the incident intensity for non-absorbing interfaces, as described qualitatively by Fresnel coefficients. These coefficients predict partial reflection at most angles, with higher reflectivity for perpendicular polarization and near-total reflection at grazing incidence, but occurs only in contexts. In catoptrics, metallic mirrors approach total reflection with minimal energy loss, preserving photon flux while directing it specularly. Reflected light exhibits either specular or diffuse characteristics depending on surface microstructure. Specular reflection occurs on smooth, polished surfaces like mirrors or calm , where incident rays reflect coherently at equal angles, preserving image sharpness and directionality. In contrast, diffuse reflection scatters light in multiple directions from rough surfaces such as or matte , due to microscopic facets redirecting rays randomly, which diffuses brightness without forming distinct images. This distinction is evident in applications: enables clear catoptric imaging, while contributes to uniform illumination in non-imaging . The remains invariant upon reflection, continuing at c=3×108c = 3 \times 10^8 m/s in or the medium's post-reflection, as the process involves no medium change or absorption. This constancy ensures that reflected wavefronts propagate without temporal distortion, a fundamental property exploited in catoptric timing and .

Mathematical Principles

Laws of Reflection

The laws of reflection form the cornerstone of catoptrics, governing the behavior of rays at a reflecting surface in geometric . These laws, first systematically articulated by around 300 BCE, ensure predictable ray paths essential for and optical design. The first law of reflection states that the incident ray, the reflected ray, and to the reflecting surface at the point of incidence all lie within the same plane. This coplanarity arises from the boundary conditions in electromagnetic theory, where the tangential components of the electric and magnetic fields must be continuous across the interface, implying that any out-of-plane component would violate these conditions. To demonstrate this mathematically using , let i⃗\vec{i}
Add your contribution
Related Hubs
User Avatar
No comments yet.