13.4: Multiple-Slit Interference
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- Jan 13, 2021
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Learning Objectives
By the end of this section, you will be able to:
- Describe the locations and intensities of secondary maxima for multiple-slit interference
Analyzing the interference of light passing through two slits lays out the theoretical framework of interference and gives us a historical insight into Thomas Young’s experiments. However, much of the modern-day application of slit interference uses not just two slits but many, approaching infinity for practical purposes. The key optical element is called a diffraction grating, an important tool in optical analysis, which we discuss in detail in chapter on Diffraction. Here, we start the analysis of multiple-slit interference by taking the results from our analysis of the double slit (N=2) and extending it to configurations with three, four, and much larger numbers of slits.
Figure
When this condition is met, 2d sin θ is automatically a multiple of λ, so all three rays combine constructively, and the bright fringes that occur here are called principal maxima. But what happens when the path length difference between adjacent slits is only λ/2? We can think of the first and second rays as interfering destructively, but the third ray remains unaltered. Instead of obtaining a dark fringe, or a minimum, as we did for the double slit, we see a secondary maximum with intensity lower than the principal maxima.

In general, for N slits, these secondary maxima occur whenever an unpaired ray is present that does not go away due to destructive interference. This occurs at (N−2) evenly spaced positions between the principal maxima. The amplitude of the electromagnetic wave is correspondingly diminished to 1/N of the wave at the principal maxima, and the light intensity, being proportional to the square of the wave amplitude, is diminished to
