Related papers: The Ptolemy-Alhazen problem and quadric surface mi…
An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze…
We study the well-known Ptolemy-Alhazen problem on reflection of light at the surface of a spherical mirror in the case when the source of light is very far from the mirror.
Given a light source, a spherical reflector, and an observer, where on the surface of the sphere will the light be directly reflected to the observer, i.e. where is the the specular point? This is known as the Alhazen-Ptolemy problem, and…
We describe light-reflection properties of spherically curved mirrors, like balls in the Christmas tree. In particular, we study the position of the image which is formed somewhere beyond the surface of a spherical mirror, when an eye…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection…
The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…
We address the phenomenon of reflection in concave spherical mirror in two contrasting approaches to optics. In his Optics (ca.165) Ptolemy applied the cathetus principle as a regulative means for explaining qualitatively effects related to…
A Platonic surface is a Riemann surface that underlies a regular map and so we can consider its vertices, edge-centres and face-centres. A symmetry (anticonformal involution) of the surface will fix a number of simple closed curves which we…
The eigenmirror problem asks: ``When does the reflection of a surface in a curved mirror appear undistorted to an observer?'' We call such a surface an {\em eigensurface} and the corresponding mirror an {\em eigenmirror}. The data for an…
Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the reflected lines got by reflection of the incident lines (Sm) on…
We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the K\"{a}hler cone of the latter. We then propose a version of mirror symmetry…
The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case…
In this paper, we study the problem of shock reflection by a wedge, with the potential flow equation, which is a simplification of the Euler System. In the work of M. Feldman and G. Chen, the existence theory of shock reflection problems…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
The main goal of the paper is to solve some problems about shadow for the sphere generalized on the case of the ellipsoid. Here, the essence of the problem is to find the the minimal number of non-overlapping balls with centers on the…
Ellipsometry is a technique whereby the measurement of the two orthogonal polarization components of light reflected at glancing incidence allows a characterization of the optical properties of a material at a particular frequency.…
We developed a formula for the law of reflection of a plane-polarized light beam from an inclined flat mirror in uniform rectilinear motion by a direct application of the Huygens-Fresnel principle. Applying the obtained formula and the…
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function…
Reflection equation for the scattering of lines moving in half-plane is obtained. The corresponding geometric picture is related with configurations of half-planes touching the boundary plane in 2+1 dimensions. This equation can be obtained…