Category: Index
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d’Alembert’s Principle
Introduction D’Alembert’s principle, named after French mathematician and physicist Jean le Rond d’Alembert, is a fundamental concept in classical mechanics. This principle extends the Newtonian mechanics to systems with constraints and allows the derivation of the equations of motion for complex systems in a generalized and systematic way. Basic Statement of d’Alembert’s Principle D’Alembert’s principle…
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De Sitter Universe
Introduction The de Sitter universe is a solution to Einstein’s field equations of general relativity, representing a cosmological model. Named after the Dutch astronomer Willem de Sitter, it describes an empty universe with a positive cosmological constant, implying a constant positive curvature of space. This universe exhibits exponential expansion, a concept that is key to…
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d’Alembert Operator
Introduction The d’Alembert operator, also known as the d’Alembertian or wave operator, is a second-order differential operator that is essential in the study of wave equations in classical field theory, electromagnetism, and quantum mechanics. The d’Alembert Operator Definition The d’Alembert operator is defined in the Minkowski spacetime, the setting for the special theory of relativity.…
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Cosmic Rays
Introduction Cosmic rays are high-energy particles that originate outside the Earth’s atmosphere. These particles, which are primarily protons, are one of the few direct pieces of evidence we have of the processes occurring in the far reaches of the universe. Basics of Cosmic Rays Cosmic rays were discovered in 1912 by physicist Victor Hess, who…
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Cerenkov Radiation
Introduction Cerenkov Radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The charged particles polarize the molecules of that medium, creating a shockwave of electromagnetic radiation. Basics of Cerenkov Radiation The phenomenon is named after Pavel Alekseyevich…
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Brewster’s Angle
Introduction Brewster’s angle, also known as the polarization angle, is a particular angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. Brewster’s Law…
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Babinet’s Principle
Introduction Babinet’s Principle, named after French physicist Jacques Babinet, is a theorem concerning diffraction in the field of optics. The principle states that the diffraction pattern from an opaque body is identical to the pattern from a hole of the same size and shape except for the overall forward beam intensity. Statement of Babinet’s Principle…
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Atomic Clock
Introduction An atomic clock is a type of clock that uses the vibrations of atoms to measure time with extreme precision. The most common type of atomic clock, the cesium atomic clock, uses the frequency of electrons transitioning between energy states in a cesium atom as its reference. Basic Principle The basic principle of an…
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Airy Disk
Introduction The Airy disk is the bright spot at the center of a pattern that is produced when a plane wave of light is diffracted by a circular aperture. It is named after the British astronomer Sir George Biddell Airy. The pattern consists of a bright central region, or disk, surrounded by a series of…