Related papers: A Lighthouse Illumination Problem
We report on the nature of prominent sources of light and shadow in the Galactic Center. With respect to the Bremsstrahlung X-ray emission of the hot plasma in that region the Galactic Center casts a 'shadow'. The 'shadow' is caused by the…
We consider the effect on the propagation of light of inhomogeneities with sizes of order 10 Mpc or larger. The Universe is approximated through a variation of the Swiss-cheese model. The spherical inhomogeneities are void-like, with…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
Given any smooth plane curve {\alpha}(s)representing a mirror that reflects light the usual way and any radiant light source at a point in the plane, the reflected light will produce a caustic envelope. For such an envelope, we show that…
We pose a natural generalization to the well-studied and difficult no-three-in-a-line problem: How many points can be chosen on an $n \times n$ grid such that no three of them form an angle of $\theta$? In this paper, we classify which…
Stray light in X-ray telescopes is a well-known issue. Unlike rays focused via a double reflection by usual grazing-incidence geometries such as the Wolter-I, stray rays coming from off-axis sources are reflected only once by either the…
Steinhaus proved that given a~positive integer $n$, one may find a circle surrounding exactly $n$ points of the integer lattice. This statement has been recently extended to Hilbert spaces by Zwole\'{n}ski, who replaced the integer lattice…
Compact objects with a light sphere such as black holes and wormholes can reflect light rays like a mirror. This gravitational lensing phenomenon is called retrolensing and it is an interesting tool to survey dark and compact objects with a…
In ["Illumination of convex bodies with many symmetries", Mathematika 63 (2017)], Tikhomirov verified the Hadwiger-Boltyanski Illumination Conjecture for the class of 1-symmetric convex bodies of sufficiently large dimension. We propose an…
The total magnification due to a point lens has been of particular interest as the theorem that gravitational lensing results in light amplification for all observers appears to contradict the conservation of photon number. This has been…
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…
In recent years, our understanding of high energy density plasmas has played an important role in improving inertial fusion confinement and in emerging new fields of physics, such as laboratory astrophysics. Every new idea required…
The simulation proposes that the cylindrical cavity around a circular light source can decreases the divergence angle without changing the emission energy and source size. This result can provide a way to reduce the etendue of the light…
Black holes are a common feature of the Universe. They are observed as stellar mass black holes spread throughout galaxies and as supermassive objects in their centres. Observations of stars orbiting close to the centre of our Galaxy…
Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. Fix $0 < \alpha < 1$. Let…
The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray…
This paper argues that there is a large population of dark galaxies which reveals its presence by the gravitational lensing of quasars, and outnumbers normal galaxies by around 3:1. There are 8 double quasars with a separation greater than…
Searching for lopsided/interacting objects among ~1500 isolated galaxies yields only eight strongly disturbed galaxies which may be explained as a result of their interaction with massive dark objects. We present results of spectral and…
The dimensionless entropy, ${\cal S} \equiv S/k$, of the visible universe, taken as a sphere of radius 50 billion light years with the Earth at its "center", is discussed. An upper limit ($10^{112}$), and a lower limit ($10^{102}$), for…
We describe here an optical device, based on time-delays, for solving the set splitting problem which is well-known NP-complete problem. The device has a graph-like structure and the light is traversing it from a start node to a destination…