2D Wave Interference. Constructive and Destructive Interference :. When waves overlap, their displacements can CANCEL or ADD UP. Out of phase- ½ Delay. In phase- 0 Delay. Result: Constructive Interference Destructive Interference. 1-D interference.
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When waves overlap, their displacements can CANCEL or ADD UP.
Out of phase- ½ Delay
In phase- 0 Delay
Result: Constructive Interference Destructive Interference
Complete destructive interference occurs when the phase delay between the waves is : ½ , 3/2 , 5/2 , 7/2 ……. Etc.
The points of destructive interference are called NODES.
2-D interference simulation
Interference of Waves in Two Dimensions :
In two dimensions, interfering waves from two sources with the same wavelength produce stationary NODAL LINES:
Source Separation, d
● Nodal lines have a hyperbolic shape but appear STRAIGHT at a distance
● Nodal line number depends on the wavelength and source separation
d , #
Waves from S1 and S2 arriving at ANY point P on the first nodal line are out of phase by
Path difference for first nodal line, n=1:
For second nodal line, n=2:
For third nodal line, n=3:
General formula for the nth nodal line:
At large distances
PS1 || PS2
Angles X 90
Sin n = AS1
AS1= dsin n
At large distances from the sources, the path
difference becomes equal todsin n
Combine with Eqn: 1:
We get a second equation with the angle of the
nth nodal line:
Where n is the nodal line number
is the wavelength
d is the source separation
is the angle of the nodal line
Sample Question 3
III. Cases wheren difficult to measure:
In some cases (e.g. light interference), the angles of the nodal lines are not easily measured.
We’ll now identify a way find the angle from distances measured on the interference pattern. nodal pattern
From Triangle BCP we can see:
We will now combine this with equation 2:
Where d- source separation * All distances in metres!
n = nodal line number
L- distance measured from the centre of S1S2 to nodal point P
X- the perpendicular distance from the centre line of the pattern
to point P
Try Sample question 4
● prior to 1802, interference of light was NOT observed
● incandescent light sources
emit incoherent light (random phase)
● very small, so nodal line spacing very small
1802- Young developed the DOUBLE SLIT experiment
● this was the deciding evidence for WAVE model of light
Bright Bands-constructive interference
Dark Bands-destructive interference
*From this pattern the easiest measurement is the node to node spacing x