HUYGENS'S PRINCIPLEWavelet Theory and Visualisation

By Paul S

HUYGENS’S WAVELETS

“In 1678, Huygens proposed that every point which a luminous

disturbance reaches becomes a source of a spherical wave; the

sum of these secondary waves determines the form of the wave

at any subsequent time.” – Wikipedia

These Secondary waves are otherwise known as wavelets and

have the same frequency and wavelength as the wave they come from.

This principle can be used to explain the propagation of light in

different circumstances.

PREDICTING A WAVEFORM

Using an excel program I designed it is possible to input a linear wave source and predict the propagation of the wave outwards.

I did this by using five three-dimensional ripples but centred at 5 different locations along the linear wave source. With 1 at each end and the other 3 equally spaced out in between.Then by looking at the interference pattern of the 5 wavelets you can approximate the resulting waveform. This is of course an approximation as the wave source would have infinite wavelets along it’s length.

Then by incrementing the “Time” value you can see how the waveform changes over time and show the wave’s propagation.

LINEAR PROPAGATION

Using this we can see how a wave propagates given an (approximately) infinite linear source. To do this I made the distance between each wavelet large enough that the ends of the wave source are outside of the visible region. (an X difference of 0.75)

This clearly shows wave fronts parallel to the wave source moving in both directions perpendicular to the wave source. This is showing linear propagation as the wave fronts do not bend or curve as they travel.

The wave fronts would become clearer if more wavelets were modelled.

DIFFRACTION

Diffraction is occurs when a wave passes through a gap which is smaller than the wave’s wavelength, this can be modelled as a linear wave source with the same length as the gap.

You can see this using the visualisation by starting from an X difference of 0.75 and slowly decreasing it until it is 0.When the X difference is 0.75 it is approximately and infinite wave source, and at 0 it is a point source.

As the X difference decreases the wave fronts become more curved, it especially starts curving after an X difference of 0.25 at which the wave source is the same length of the wavelength, until at a point source the waveform is perfectly circular.

Almost circular wave front

REFRACTION

Refraction occurs due to a wave entering a different medium and travelling at a different speed. Due to this change in speed the wave will change direction if it enters the medium at an angle.

This can be shown using wavelet theory according to the diagram below.When the wave fronts meet the new medium they act as wavelet sources along the edge of the medium but as the waves meet the new medium at different times and therefore change speed at different times there is a time difference between each wavelet.

REFRACTION VISUALISED

In order to show refraction in the excel program requires the

code to be modified to include a time difference between each

wavelet.

In the image below you can see that the wave fronts of the

waveform are not parallel to the wave source as the wave source is acting as the edge of the two mediums. And a

refracted wave will never be parallel to the edge of the two

mediums.

0.9 1.05 1.2 1.35 1.5 Time

-0.00449 0.487159 0.879129 0.99358 0.723265 0

-0.71813 -0.24709 0.346053 0.841584 0.99358 y dif

-1 -0.82877 -0.32655 0.346053 0.879129 0

-0.74145 -0.99552 -0.82877 -0.24709 0.487159 x dif

-0.14272 -0.74145 -1 -0.71813 -0.00449 0

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

Only change the green tiles manually.

Time X Difference

0 0

Y Difference

0

-1.5

-0.75

0

0.75

1.5

-1.5 -0.75 0 0.75 1.5

Wave Source

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 2

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 3

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 4

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 5

-1

-0.5

0

0.5

1

-1.5

-1.05

-0.6

-0.15

0.3

0.75

1.2

Waveform from Interference

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Central Wavelet

By changing the X and Y distances between each of the 5 wavelets will effect the Interference pattern in a similar way to deacreasing/increasing the diffraction gap. Increase the time to see the propogation of the wave.

Increase Time

0.9 1.05 1.2 1.35 1.5 Time

-0.00449 0.487159 0.879129 0.99358 0.723265 0

-0.71813 -0.24709 0.346053 0.841584 0.99358 y dif

-1 -0.82877 -0.32655 0.346053 0.879129 0

-0.74145 -0.99552 -0.82877 -0.24709 0.487159 x dif

-0.14272 -0.74145 -1 -0.71813 -0.00449 0

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

Only change the green tiles manually.

Time X Difference

0 0

Y Difference

0

-1.5

-0.75

0

0.75

1.5

-1.5 -0.75 0 0.75 1.5

Wave Source

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 2

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 3

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 4

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 5

-1

-0.5

0

0.5

1

-1.5

-1.05

-0.6

-0.15

0.3

0.75

1.2

Waveform from Interference

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Central Wavelet

By changing the X and Y distances between each of the 5 wavelets will effect the Interference pattern in a similar way to deacreasing/increasing the diffraction gap. Increase the time to see the propogation of the wave.

Increase Time

0.9 1.05 1.2 1.35 1.5 Time

-0.00449 0.487159 0.879129 0.99358 0.723265 0

-0.71813 -0.24709 0.346053 0.841584 0.99358 y dif

-1 -0.82877 -0.32655 0.346053 0.879129 0

-0.74145 -0.99552 -0.82877 -0.24709 0.487159 x dif

-0.14272 -0.74145 -1 -0.71813 -0.00449 0

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

Only change the green tiles manually.

Time X Difference

0 0

Y Difference

0

-1.5

-0.75

0

0.75

1.5

-1.5 -0.75 0 0.75 1.5

Wave Source

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 2

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 3

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 4

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 5

-1

-0.5

0

0.5

1

-1.5

-1.05

-0.6

-0.15

0.3

0.75

1.2

Waveform from Interference

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Central Wavelet

By changing the X and Y distances between each of the 5 wavelets will effect the Interference pattern in a similar way to deacreasing/increasing the diffraction gap. Increase the time to see the propogation of the wave.

Increase Time

0.9 1.05 1.2 1.35 1.5 Time

-0.00449 0.487159 0.879129 0.99358 0.723265 0

-0.71813 -0.24709 0.346053 0.841584 0.99358 y dif

-1 -0.82877 -0.32655 0.346053 0.879129 0

-0.74145 -0.99552 -0.82877 -0.24709 0.487159 x dif

-0.14272 -0.74145 -1 -0.71813 -0.00449 0

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

Only change the green tiles manually.

Time X Difference

0 0

Y Difference

0

-1.5

-0.75

0

0.75

1.5

-1.5 -0.75 0 0.75 1.5

Wave Source

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 2

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 3

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 4

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 5

-1

-0.5

0

0.5

1

-1.5

-1.05

-0.6

-0.15

0.3

0.75

1.2

Waveform from Interference

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Central Wavelet

By changing the X and Y distances between each of the 5 wavelets will effect the Interference pattern in a similar way to deacreasing/increasing the diffraction gap. Increase the time to see the propogation of the wave.

Increase Time

0.9 1.05 1.2 1.35 1.5 Time

-0.00449 0.487159 0.879129 0.99358 0.723265 0

-0.71813 -0.24709 0.346053 0.841584 0.99358 y dif

-1 -0.82877 -0.32655 0.346053 0.879129 0

-0.74145 -0.99552 -0.82877 -0.24709 0.487159 x dif

-0.14272 -0.74145 -1 -0.71813 -0.00449 0

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

0.9 1.05 1.2 1.35 1.5

-0.00449 0.487159 0.879129 0.99358 0.723265

-0.71813 -0.24709 0.346053 0.841584 0.99358

-1 -0.82877 -0.32655 0.346053 0.879129

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-0.14272 -0.74145 -1 -0.71813 -0.00449

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.809017 0.951057 0.309017 -0.58779 -1

0.852359 0.928242 0.252712 -0.6292 -0.9989

0.948467 0.837471 0.082018 -0.74145 -0.98263

0.999234 0.6259 -0.19725 -0.8853 -0.91512

0.871218 0.252712 -0.5445 -0.98987 -0.74782

0.473266 -0.25081 -0.86105 -0.96143 -0.44247

-0.14272 -0.74145 -1 -0.71813 -0.00449

-0.74145 -0.99552 -0.82877 -0.24709 0.487159

-1 -0.82877 -0.32655 0.346053 0.879129

-0.71813 -0.24709 0.346053 0.841584 0.99358

-0.00449 0.487159 0.879129 0.99358 0.723265

Only change the green tiles manually.

Time X Difference

0 0

Y Difference

0

-1.5

-0.75

0

0.75

1.5

-1.5 -0.75 0 0.75 1.5

Wave Source

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 2

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 3

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 4

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Wavelet 5

-1

-0.5

0

0.5

1

-1.5

-1.05

-0.6

-0.15

0.3

0.75

1.2

Waveform from Interference

-1.5-1.2

-0.9-0.6

-0.30

0.30.6

0.91.2

1.5

-1

-0.5

0

0.5

1

-1.5

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

1.5

Central Wavelet

By changing the X and Y distances between each of the 5 wavelets will effect the Interference pattern in a similar way to deacreasing/increasing the diffraction gap. Increase the time to see the propogation of the wave.

Increase Time