Interference and Diffraction

This looks odd. A football player is kicking balls towards a wall with two gaps in it. Notice how the balls pile up in the net as they go through the two gaps.

We recall that whenerver a wave passes through an aperture, it diffracts. The narrower the gap, the greater the diffraction. When there are two slits, their diffraction contributions add together. A bright fringe is formed when the contributions superpose constructively, having a path difference of a whole number of wavelengths, a dark fringe when the path difference is an odd number of half wavelengths.

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Click on the link for an explanation and the equations.

Young’s slit theory. Evidence for light as a wave.

It’s helpful to think about these ideas using Huygen’s geometry of secondary wavelets. A plane wave produces, it seems, a linear ripple, which we might think of as millions of circular ripples moving outwards at the same speed from very closely packed point sources. In this treatment of Young’s two slits, we assume that there is a central point source at the centre of each slit. In the diagram, (a) is a single source which produces two COHERENT sources at b and c. Make sure you understand that coherent sources are either in phase or have a constant phase difference and are at the same frequency – produced here by (a)Screen Shot 3.png

Each slit contributes its own diffraction pattern. Where these overlap, interference occurs, or superposition of amplitude. The two slit interference fringes lie underneath the diffraction envelope and where the interference fringes lie underneath the diffraction minima, we don’t see them – so-called “missing orders”.Screen Shot.png

Looking at the central bright diffraction maximum – the interference fringes are evenly spaced underneath it, like this:

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Young’s method can be used to find the wavelength of the incident light – approximately. It’s approximate because we can’t accurately determine the exact centre of a bright fringe.

Finally – this interactive is required reading. Go to the Wolfram Demonstration page

Download the Wolfram CDF player and load up the demonstration “Intensity Distribution for Multiple Slit Diffraction” With 2 slits; it looks like this…You can change all the important parameters – slit width and slit separation.

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