Ripple-tank simulations: Double-Slit Interference

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Illustration of double-slit interference

Conditions and pertinent physics

1. Point Sources A pair of point sources are in phase and each radiate outgoing circular waves. The point-sources are positioned at (-1,0) and (+1,0) in the coordinate system shown.

2. Superposition The two separate outgoing circular wave patterns overlap in space and therefore interfere.

3. Interference Due to destructive interference, nodes are created. Similarly, constructive interference gives rise to antinodes. Any point on an antinode is nearer to one source than the other by exactly m wavelengths where m is an integer. This makes the two waves add in phase (and therefore tend to reinforce each other). Any point on a node is nearer to one source than the other by exactly (m + 1/2) wavelengths where m is an integer. This makes the two waves add 180° out of phase (and therefore tend to cancel). 3-D view of the above.

Questions:

In the animation above:
1. Far from the sources, the nodes and antinodes are lines which appear to diverge from the origin at specific angles (meaure angle relative to the original ``forward'' direction which in this case is -y dir). Identify all of the nodes and antinodes in the above simulation. Label them appropriately (e.g., m = 0, m =+1, etc.)
2. Determine the wavelength l and the value of d (separation between the point-sources) for the above simulation through a careful examination of the figure. (Assume the axes are calibrated in meters.)
3. Based on the wavelength and d values, compute the angles for all antinodes shown in the figure. Repeat for all nodes. Compare your results to the actual geometry of the figure.