This is an expanded and refined applet compared to my earlier applet.
The applet visualises the interference pattern created by two wave sources oscillating coherently with no initial phase shift.
The resulting hyperbolic interference lines are modeled mathematically using the distance b between the sources and the wavelength λ of the radiation. It takes into account the principle that the path difference Δ must be less than the distance b between the sources. If Δ≥b, the triangle inequality would be violated, making it physically impossible to find a point that satisfies this condition and therefore rendering interference impossible.
It is shown that in the limiting transition (from near to far field), the hyperbolas of the interference pattern transform into straight lines: y=x*sqrt((b/(r*λ))2-1), where r takes on integer and half-integer values. These lines correspond to the far-field approximation, in which the path difference is given by Δ=b* sin(θ).
Explore the formulas provided in the applet. Examine the effect of changing the b, λ and r model parameter sliders on the characteristics of the resulting interference pattern in the near and far fields. The applet uses the distance between two points on the screen, B(r) and Z(r), as a measure for assessing the boundaries of these fields. Point B(r) is on the asymptote and point Z(r) is on the corresponding hyperbola. In the limit, i.e. when y (distance to the screen) approaches infinity, they should coincide. Explore how this distance changes on the screen for different interference orders.
The previous applet provides the ability to explore constructive and destructive interference curves from two point sources.
Formulas used in the applet:
A near-field and far-field interference applet simulation by two coherent radiation sources
Hyperbolic lines of Two-Beam Interference
Distribution of radiation intensity in the interference pattern from two coherent sources in the a) near field and b) far field
Distribution of radiation intensity in the interference pattern from two coherent sources in the
a) near field
b) far field.
In contrast to interference in the near field, in the far field
-the asymptote is a linear function that practically coincides with the hyperbolas of constructive and destructive interference,
-the spacing of the fringes increases with distance from the sources.
