相关论文: Images in Christmas Balls
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 discuss the problem of the reflection of light on spherical and quadric surface mirrors. In the case of spherical mirrors, this problem is known as the Alhazen problem. For the spherical mirror problem, we focus on the reflection…
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.
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
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…
Students in introductory physics courses struggle to understand virtual image formation by a plane mirror and the proper construction of ray diagrams. This difficulty, if not sufficiently addressed, results in further problems throughout…
The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball,…
We design freeform lenses refracting an arbitrarily given incident field into a given fixed direction. In the near field case, we study the existence of lenses refracting a given bright object into a predefined image. We also analyze the…
The displacement of star images by atmospheric refraction observed by an Earth-bound telescope is dominated by a familiar term proportional to the product of the tangent of the zenith angle by the refractivity at the ground. The manuscript…
Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is…
An ellipsoid is the image of a ball under an affine transformation. If this affine transformation is over the complex numbers, we refer to it as a complex ellipsoid. Characterizations of real ellipsoids have received much attention over the…
We model the light-curves from radiation-driven clouds near an accreting black hole. Taking into account the multiple images due to strong gravitational lensing, we find that sharp spikes can significantly enhance the observed flux.…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
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…
Nearly a decade ago it was discovered that the spherical cell body of the alga $Chlamydomonas~reinhardtii$ can act as a lens to concentrate incoming light onto the cell's membrane-bound photoreceptor and thereby affect phototaxis. Since…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
The light distribution on the focal surface of spheric mirrors designed for telescopes in the lens-less Schmidt configuration is calculated analytically using geometrical optics. This analysis was motivated by considerations of the design…
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…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We…