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Related Concept Videos

Hyperbolas01:30

Hyperbolas

A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse axis is...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
Hyperbolic Functions01:26

Hyperbolic Functions

A flexible cable suspended between two points at the same height naturally forms a curve known as a catenary. This shape results from the balance between the cable’s weight and the tension acting along its length, representing a state of mechanical equilibrium. Unlike simpler approximations, the true shape of a hanging cable is described using hyperbolic functions.Hyperbolic functions are closely related to exponential functions and are named for their connection to the geometry of the...
Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
Reflective Property of Parabolas01:26

Reflective Property of Parabolas

A parabola is a basic type of conic section that results from the intersection of a plane with a double-napped cone in a direction parallel to one of the cone's sides. This U-shaped curve has a distinctive reflective property: all incoming rays parallel to its axis of symmetry are directed toward a single point, known as the focus. This property is widely utilized in optical and communication technologies that require precise signal concentration.In analytic geometry, a parabola is defined as...
Parabolas01:30

Parabolas

A parabola is a fundamental curve in the family of conic sections arising from the intersection of a plane with a double-napped cone when the plane is parallel to the cone’s slant height. This geometric condition yields a unique open curve defined by its equidistance from a fixed point, the focus, and a fixed line, the directrix.A parabola is mathematically defined as the locus of all points in a plane that are equidistant from the focus and the directrix. In Cartesian coordinates, the standard...

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Updated: Jun 21, 2026

Fabrication and Characterization of Superconducting Resonators
10:26

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

Hyperbolic cone-channel condenser.

H P Gush1

  • 1Department of Physics, University of British Columbia, Vancouver, BC, Canada.

Optics Letters
|August 15, 2009
PubMed
Summary

This study details a novel optical condensing system using a hyperbolic cone and lens for efficient light concentration. The design achieves optimal light density in a compact form, with potential simplification for specific applications.

Area of Science:

  • Optical engineering
  • Illumination systems design

Background:

  • Efficient light concentration is crucial for various optical applications.
  • Existing systems often face limitations in compactness and performance.

Purpose of the Study:

  • To introduce a novel optical condensing system.
  • To achieve optimum light concentration within a compact design.

Main Methods:

  • The system comprises a lens and a polished cone interior.
  • The cone's shape is generated by rotating a hyperbola around an axis.

Main Results:

  • The hyperbolic cone design enables optimum light concentration.
  • The system is relatively compact.
  • Under specific conditions, the hyperbola simplifies to a straight line, easing construction.

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Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
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Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

Published on: October 5, 2018

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Last Updated: Jun 21, 2026

Fabrication and Characterization of Superconducting Resonators
10:26

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
10:03

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

Published on: October 5, 2018

Conclusions:

  • The described optical condensing system offers an effective solution for light concentration.
  • Its compact nature and potential for simplified construction make it advantageous.