spherical aberration

Examples of spherical aberration in the following topics:

• Aberrations

  • A chromatic aberration, also called achromatism or chromatic distortion, is a distortion of colors .
  • This aberration happens when the lens fails to focus all the colors on the same convergence point .
  • A comatic aberration, or coma, occurs when the object is off-center.
  • These aberrations can cause objects to appear pear-shaped.
  • Spherical aberrations are a form of aberration where rays converging from the outer edges of a lens converge to a focus closer to the lens, and rays closer to the axis focus further.

• The Telescope

  • The potential advantages of using mirrors instead of lenses were a reduction in spherical aberrations and the elimination of chromatic aberrations.
  • With the invention of achromatic lenses in 1733, color aberrations were partially corrected, and shorter, more functional refracting telescopes could be constructed.

• Combinations of Lenses

  • The use of multiple elements allows for the correction of more optical aberrations, such as the chromatic aberration caused by the wavelength-dependent index of refraction in glass, than is possible using a single lens.
  • In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations.
  • An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration.
  • The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.
  • (a) Chromatic aberration is caused by the dependence of a lens's index of refraction on color (wavelength).

• Spherical and Plane Waves

  • Spherical waves come from point source in a spherical pattern; plane waves are infinite parallel planes normal to the phase velocity vector.
  • In 1678, he proposed that every point that a luminous disturbance touches becomes itself a source of a spherical wave; the sum of these secondary waves determines the form of the wave at any subsequent time.
  • Since the waves all come from one point source, the waves happen in a spherical pattern.
  • All the waves come from a single point source and are spherical .
  • When waves are produced from a point source, they are spherical waves.

• Gravitational Attraction of Spherical Bodies: A Uniform Sphere

  • The Shell Theorem states that a spherically symmetric object affects other objects as if all of its mass were concentrated at its center.
  • For highly symmetric shapes such as spheres or spherical shells, finding this point is simple.
  • A spherically symmetric object affects other objects gravitationally as if all of its mass were concentrated at its center,
  • If the object is a spherically symmetric shell (i.e., a hollow ball) then the net gravitational force on a body inside of it is zero.
  • That is, a mass $m$ within a spherically symmetric shell of mass $M$, will feel no net force (Statement 2 of Shell Theorem).

• Introduction to Spherical and Cylindrical Harmonics

  • In this section we will apply separation of variables to Laplace's equation in spherical and cylindrical coordinates.
  • Spherical coordinates are important when treating problems with spherical or nearly-spherical symmetry.
  • To a first approximation the earth is spherical and so is the hydrogen atom, with lots of other examples in-between.
  • On the other hand, if we tried to use Cartesian coordinates to solve a boundary value problem on a spherical domain, we couldn't represent this as a fixed value of any of the coordinates.
  • Obviously this would be much simpler if we used spherical coordinates, since then we could specify boundary conditions on, for example, the surface $x = r \cos \phi \sin \theta$ constant.

• Spherical Distribution of Charge

  • The charge distribution around a molecule is spherical in nature, and creates a sort of electrostatic "cloud" around the molecule.
  • This distribution around a charged molecule is spherical in nature, and creates a sort of electrostatic "cloud" around the molecule.
  • The attraction or repulsion forces within the spherical distribution of charge is stronger closer to the molecule, and becomes weaker as the distance from the molecule increases.
  • Describe shape of a Coulomb force from a spherical distribution of charge

• Adding velocities

  • This is the aberration equation.

• Newton's Rings

  • Newton's rings are a series of concentric circles centered at the point of contact between a spherical and a flat surface.
  • In 1717, Isaac Newton first analyzed an interference pattern caused by the reflection of light between a spherical surface and an adjacent flat surface.
  • Newton's rings appear as a series of concentric circles centered at the point of contact between the spherical and flat surfaces.
  • A spherical lens is placed on top of a flat glass surface.

• Image Formation by Spherical Mirrors: Reflection and Sign Conventions

  • This section will cover spherical mirrors.
  • Spherical mirrors can be either concave or convex.