plane

Examples of plane in the following topics:

• 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.
  • A plane wave is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector .
  • It is not possible in practice to have a true plane wave; only a plane wave of infinite extent will propagate as a plane wave.
  • However, many waves are approximately plane waves in a localized region of space.
  • Plane waves are an infinite number of wavefronts normal to the direction of the propogation.

• Image Reflection by a Plane Mirror

  • The most common mirrors are flat and called plane mirrors.
  • In flat, or plane mirrors, the image is a virtual image, and is the same distance behind the mirror as the object is in front of the mirror.
  • Draw the plane mirror as a straight line on a principal axis.

• Rolling Without Slipping

  • When an object is rolling on a plane without slipping, the point of contact of the object with the plane does not move.
  • If we imagine a wheel moving forward by rolling on a plane at speed v, it must also be rotating about its axis at an angular speed $\omega$ since it is rolling.
  • A body rolling a distance of x on a plane without slipping.

• Transverse Waves

  • If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y–z plane.
  • Here we observe that the wave is moving in t and oscillating in the x-y plane.
  • In the figure we observe this motion to be in x-y plane (denoted by the red line in the figure).
  • Examples of transverse waves include seismic S (secondary) waves, and the motion of the electric (E) and magnetic (M) fields in an electromagnetic plane waves, which both oscillate perpendicularly to each other as well as to the direction of energy transfer.

• Thomson Scattering

  • The electric field of the radiated wave is in the plane containing ${\bf E}_{wave}$ and $ {\bf n}$.
  • The first term in the expression corresponds to light polarized in the plane containing ${\bf E}_{w,1}$ and ${\bf n}$ and the second term traces light polarized in the plane containing ${\bf E}_{w,2}$ and ${\bf n}$.
  • More energy is scattered into the ${\bf E}_{w,1}-{\bf n}$ plane than in the other in the ratio of $1:\cos^2 \theta$, so the scattered radiation is polarized with

• Normal Forces

  • A more complex example of a situation in which a normal force exists is when a mass rests on an inclined plane.
  • A mass rests on an inclined plane that is at an angle $\theta$ to the horizontal.

• Quantum Tunneling

  • Between the two lobes there is a nodal plane.
  • By definition there is precisely 0 probability of finding an electron anywhere along that plane, and because the plane extends infinitely it is impossible for an electron to go around it.
  • But what accounts for the difference in probability of an electron tunneling over a nodal plane and a ball tunneling through a brick wall?

• Conditions for Wave Interference: Reflection due to Phase Change

  • A simple form of wave interference is observed when two waves of the same frequency (also called a plane wave) intersect at an angle , as shown in .

• Average Velocity: A Graphical Interpretation

  • Suppose, for example, an airplane passenger took five seconds to move -4 m (the negative sign indicates that displacement is toward the back of the plane).
  • The minus sign indicates that the average velocity is also toward the rear of the plane.
  • For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he gets to the back of the plane.

• Linear Momentum

  • If two particles were moving on a plane we would choose our xy-plane to be on the plane of motion.