The interference pattern shown above was first observed for visible light in 1801 by Thomas Young Young, the experiment is still sometimes called Young's slit experiment.
exclamation In the above description we have assumed the incident light is monochromatic. If white light (containing all the wavelengths in the visible spectrum) is used, the maxima for the different wavelengths will occur at slightly different positions (y) on the screen. In this case an interference pattern will only be observed if the maximum - minimum separation is much larger than the separation between the maxima of the extreme wavelengths in white light (red and violet) for the same "n".
In the above description we have shown that at certain locations on the screen there will be bright spots whereas at other locations there will be no light - the interference pattern. But exactly how does the light intensity vary as a function of position on the screen ?
In the diagram at the top of this page the electric field from light originating at each of the slits S1 and S2 can be written,
Therefore the E field at P can be written,
The product of an amplitude and a sinusoidal time varying wave. In the case of light waves the frequency of the time varying part is so large that our eyes and most instruments "see" only the ampliutde part. Actually, what we observe is the intensity, which is the square of the amplitude. The intensity observed at P is then given by,
as shown in the red shading in the diagram above. Note that maxima of the above cosine squared function occur when φ = 2π n; this leads to bright spots on the screen.
As we have seen, when the path difference is an integer multiple of wavelengths, the waves from the two sources interefer constructively. That is they are in phase, and as we have seen above, φ must be an integer multiple of 2π,
Thus for small values of θ (sinθ = θ), φ and θ are proportional to each other.