polar

Examples of polar in the following topics:

• Polarization By Scattering and Reflecting

  • In the previous atom we discussed how polarized lenses work.
  • The reflected light is more horizontally polarized.
  • Just as unpolarized light can be partially polarized by reflecting, it can also be polarized by scattering (also known as Rayleigh scattering; illustrated in ).
  • The light parallel to the original ray has no polarization.
  • The light perpendicular to the original ray is completely polarized.

• Total Polarization

  • When light hits a surface at a Brewster angle, reflected beam is linearly polarized. shows an example, where the reflected beam was nearly perfectly polarized and hence, blocked by a polarizer on the right picture.
  • A polarizing filter allows light of a particular plane of polarization to pass, but scatters the rest of the light.
  • When two polarizing filters are crossed, almost no light gets through.
  • In the picture at left, the polarizer is aligned with the polarization angle of the window reflection.
  • In the picture at right, the polarizer has been rotated 90° eliminating the heavily polarized reflected sunlight.

• Converting Between Polar and Cartesian Coordinates

  • Polar and Cartesian coordinates can be interconverted using the Pythagorean Theorem and trigonometry.
  • When given a set of polar coordinates, we may need to convert them to rectangular coordinates.
  • There are other sets of polar coordinates that will be the same as our first solution.
  • A right triangle with rectangular (Cartesian) coordinates and equivalent polar coordinates.
  • Derive and use the formulae for converting between Polar and Cartesian coordinates

• Polarization By Passing Light Through Polarizers

  • Since the direction of polarization is parallel to the electric field, you can consider the blue arrows to be the direction of polarization.
  • What happens to these waves as they pass through the polarizer?
  • Lets call the angle between the direction of polarization and the axis of the polarization filter θ.
  • If you pass light through two polarizing filters, you will get varied effects of polarization.
  • A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its direction.

• Bond Polarity

  • Molecular polarity is dependent on the presence of polar covalent bonds and the molecule's three-dimensional structure.
  • Such bonds are said to be 'polar' and possess partial ionic character.
  • Molecular polarity: when an entire molecule, which can be made out of several covalent bonds, has a net polarity, with one end having a higher concentration of negative charge and another end having a surplus of positive charge.
  • A polar molecule acts as an electric dipole which can interact with electric fields that are created artificially, or that arise from interactions with nearby ions or other polar molecules.
  • The water molecule, therefore, is polar.

• Bond Polarity

  • Bond polarity exists when two bonded atoms unequally share electrons, resulting in a negative and a positive end.
  • Bonds can fall between one of two extremes, from completely nonpolar to completely polar.
  • The terms "polar" and "nonpolar" usually refer to covalent bonds.
  • To determine the polarity of a covalent bond using numerical means, find the difference between the electronegativity of the atoms; if the result is between 0.4 and 1.7, then, generally, the bond is polar covalent.
  • The hydrogen fluoride (HF) molecule is polar by virtue of polar covalent bonds; in the covalent bond, electrons are displaced toward the more electronegative fluorine atom.

• Conics in Polar Coordinates

  • Polar coordinates allow conic sections to be expressed in an elegant way.
  • In this section, we will learn how to define any conic in the polar coordinate system in terms of a fixed point, the focus $P(r,θ)$ at the pole, and a line, the directrix, which is perpendicular to the polar axis.
  • Thus, each conic may be written as a polar equation, an equation written in terms of $r$ and $\theta$.
  • For a conic with a focus at the origin, if the directrix is $x=±p$, where $p$ is a positive real number, and the eccentricity is a positive real number $e$, the conic has a polar equation: $r=\frac{ep}{1\: \pm\: e\: \cos\theta}$
  • For a conic with a focus at the origin, if the directrix is $y=±p$, where $p$ is a positive real number, and the eccentricity is a positive real number $e$, the conic has a polar equation: $r=\frac{ep}{1\: \pm\: e\: \sin\theta}$

• Introduction to the Polar Coordinate System

  • Polar coordinates are points labeled $(r,θ)$ and plotted on a polar grid.
  • In mathematical literature, the polar axis is often drawn horizontal and pointing to the right.
  • The polar grid is scaled as the unit circle with the positive $x$-axis now viewed as the polar axis and the origin as the pole.
  • Even though we measure $θ$ first and then $r$, the polar point is written with the $r$ -coordinate first.
  • Points in the polar coordinate system with pole $O$ and polar axis $L$.

• Polar Coordinates

  • Such definitions are called polar coordinates.
  • The angle is known as the polar angle, or radial angle, and is usually given as $\theta$.
  • The polar axis is usually drawn horizontal and pointing to the right .
  • Polar coordinates in $r$ and $\theta$ can be converted to Cartesian coordinates $x$ and $y$.
  • A set of polar coordinates.

• Polarization

  • $For example a wave can be linearly polarized with its electric field always pointing along $\epsilon_1$ or along $\epsilon_2$.
  • If this phase difference is zero, then the wave is linearly polarized (left panel of Fig.2.1) with the polarization vector making an angle $\theta=\tan^{-1}(E_2/E_1)$ with $\epsilon_1$ and a magnitude of $E=\sqrt{E_1^2+E_2^2}.$
  • One could have defined an alternative representation based on the circular polarizations
  • Often it is convenient to use this circular polarization basis rather than the linear polarization basis above (for example, waves traveling through plasma).
  • It is possible to recover this polarization information through intensity measurements.