two-source interference

• Waves from sources spread out in circles from their source, meet each other and interfere.

  
  

  Crest meets crest or trough meets trough -> constructive interference (antinode)

  Crest meets trough -> deconstructive interference (node)

  
  

  As waves spread out crests and troughs mix creating interference

  patterns -> special patterns occur if both waves have same frequency, travelling through same medium so same velocity therefore same wavelength.

  antinodes appear in lines called antinodal lines. Nodes appear in lines called nodal lines

  
• When two waves spread out from their sources and interfere, they produce lines of nodes and antinodes.

  
  

  If a point is a whole number of wavelengths from both sources (1λ,2λ,3λ) it will be an antinode.

  
  

  If a point is a whole number of wavelengths from one source but a fractional number of wavelengths from the other (1/2λ, 3/2λ, 5/2λ) it will be a node
• If a person walks across these nodal and antinodal lines, they will hear it alternate from quiet to loud. It will be quiet on the nodal lines because of destructive interference and loud on antinodal lines because of constructive interference
•  Diffraction -> waves go through a hole in a wall and spread out like circles. This spreading out is called diffraction

  The wavelength has to be a similar size to the slit. If wavelength is totally different (bigger or smaller) No diffraction happens

  
• A wave comes in and hits a wall. There are two slits in the wall. The wave goes through the slits.

  If the wavelength is similar to the slit width, then

  diffraction will happen. It will happen twice -> creating two sources -> get two-source interference pattern
• wave is light -> antinodal points it will be extra bright (bright fringes)

  -> nodal points it will be dark (dark fringes)

  this creates alternating pattern of dark and bright spots

  Light with different frequencies spreads out different amounts, creating different patterns, Light of the same colour has the same frequency and wavelength

  
• d sin(θ) = nλ

  distance between the waves is a whole number of wavelengths

  describing constructive interference (bright fringes) on the screen

  gives position of bright fringes
•  d sin(θ) = (n + 1/2)λ

  distance between waves isn't a whole number of wavelengths

  describing deconstructive interference (dark fringes) on the screen

  gives position of dark fringes 
• nλ =dx/L

  gives the distance to a bright fringe.

  
  

  based on an assumption that d is much smaller than L
• Bright spots (maxima)

  The maximum in the middle is called the central maximum. at that point on the screen, n = 0. The phase difference is 0. Either side of the 0th order maximum are the first order maxima, n = 1. Then the two 2nd order maxima and so on. n is the order of whatever maximum you’re looking at. It’s the same with minima (dark spots). The intensity of the maxima decreases as you go out from the 0th order maximum too.

  
• Diffraction gratings are made from several hundred to several thousand slits. more slits -> more interference can occur and the maxima are brighter (than the double slit).

  The bright fringes (maxima)

  are still the same distance apart.
• Different frequencies are diffracted differently

  Low frequencies (e.g. red light) are diffracted more. High frequencies (e.g. blue light) are diffracted less.

  This causes red to be on the outside of the blue in the rainbows

  No diffraction occurs in central fringe – light goes straight through. Meaning individual colours of white light met up in phase at the centre of the screen and form white light.