Interference and Diffraction

Definitions and General Principles
Phase: Position within a points cycle of oscillation on a wave (° or c)

Path difference: The difference in the distance travelled by two coherent waves from different sources (m)

Interference: The superposition of two or more waves
 * Constructive interference occurs when the original waves add to give a resultant wave with a greater displacement (amplitude) than the original waves
 * At a path difference of nλ
 * In phase - At a phase difference of 2π (causing maximum amplitudes/bright fringes/etc)
 * Destructive interference occurs when the original waves add to give a resultant wave with a smaller displacement (amplitude) than the original waves (ie the waves cancel)
 * At a path difference of (n + 1/2)λ
 * In Antiphase - At a phase difference of π, half a cycle out of phase with another wave (producing minimum amplitudes/dark fringes/etc)A-phy-osdiff-dia09d.gif

Maximum amplitude occurs at P if:  S2P - S1P = nλ

Minimum amplitude occurs at P if:   S2P - S1P = (n + 1/2)λ

Diffraction: Spreading out of a wave as it passes through a gap (aperture), or around an obstacle
 * Maximum diffraction occurs when the gap = λ
 * When the gap > λ, little diffraction occurs
 * When the gap < λ, diffraction occurs with low intensity (most of the wave is reflected)
 * As the wave spreads out, the intensity is weakened

Huygens' Principle & Single Slit Interference
Every point on a wavefront is a point source that spreads out spherically; the new wavefront is the surface that is tangential to these. If a wave passes through a single slit (aperture), it will diffract.

There will be a pattern produced (due to Huygens' principle), of a central bright fringe, and alternating dark and bright fringes either side, which can be shown as intensity on a graph.

How much the pattern is spread depends on how the wavelength compares to the slit width, longer wavelengths will produce wider diffraction patterns.

Huygens' principle can also be used to demonstrate diffraction around obstacles/objects.

Young's Double Slit & Diffraction gratings
For multiple slits, a coherent source must be used. This can be achieved by: An interference pattern will be produced, as before an intensity graph can be plotted from this. The more slits you add (after 2 slits) won't affect the pattern of the bright and dark spots. Increasing the number of slits increases the intensity, and decreases the width of the bright spots (maximum amplitude).
 * Passing the source through a single slit first
 * Ensuring the slits are closely spaced enough that the source can fit over all of them
 * Connecting the sources (ie for speakers to the same oscillator)

nλ = dsinθ
 * n = order of the fringe
 * d = slit spacing
 * θ = angle between zero and nthorder (RADIANS)

If given the number of slits per metre (N), the slit spacing (d) = 1/N

Electron diffraction

 * Electrons interact with the spaces between the atoms in graphite
 * Diffraction patterns and interference are observed
 * Atom spacing ≈ λ
 * Diffraction and interference are wave behaviours
 * Therefore electrons show wave like properties
 * Slower electrons give wider spaced rings