Animated Mathcad plots of circular wave function defined in worksheet above.
ABOVE: Profile along the x axis, verifying formula, Wavelength set to 5 cm. Field of view set to 1 meter right and left of origin.
RIGHT: Animation of full wave using Mathcad FRAME counter. FRAME = number of still images making up the movie. Here FRAME is set to 100 total frames, displayed at 10 frames per second.
Superimposing multiple circular waves, with origins of waves spread along a vertical line:
3 wave sources in a vertical row
11 wave sources in a vertical row
41 wave sources in a vertical row
81 wave sources in a vertical row
Animation of beam shrinking in width:
Zoomed in animation of 81 wave sources in a vertical row. At the beginning of the animation, the row is 1/2 meter (50 cm) tall. At the end of the 100 frame animation, the row length is zero (all 81 sources are at the same point).
Note how the initial “beams” diverge to become almost circular by frame 90. At that point, the sources span a row about 5 cm long. This corresponds to the wavelength of the wave. All waves start to diverge strongly when they are confined to beams less than one wavelength in width. This is known as “diffraction limited focusing” and it is the reason light image based microfabrication techniques fail below light wavelength dimensions.
Animation of shrinking gap between two beams:
Animation of shrinking gap between two beams. This emulates the situation produced when a particle blocks part of a large beam. Relevant equations from the Mathcad worksheet:
The two rows of sources (top and bottom) actually merge together at the very end of the animation. But the gap between the two beams starts to fill in when the sources are still about one wavelength apart (85-90% through the animation). At that point, the two beams effectively spill over filling in the missing wave. The same thing happens with a light scattering particle. It blocks off part of the beam. But if it is smaller than the beam's wavelength, the beams to its side fill in the gap it creates, and it almost disappears. This is why nanoparticles are used in sun block!