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# Multiple Slit Diffraction/Interference - Diffraction Gratings

" Physics is actually too hard for physicists"
David Hilbert (Mathematician)

- IMPORTANT: Don't be confused, diffraction and interference are different aspects of the same phenomenon - the superposition of waves.

> Interference: Superposition of waves from a finite number of "point" sources.

> Diffraction: Superposition of waves from an infinite number of "point" sources, comprising a single large source.

- Having discussed double slit interference/diffraction, the natural extension is to 3, 4, 5... multiple slits.

> The diagram at right illustrates a 5 slit configuration, where the path difference at point P between waves from each of the slits is dsinθ with a slit separation of "d". Clearly, if the waves from all five slits are in phase, maximum intensity will be observed at P when

> where n = 0, 1, 2,...

- A detailed mathematical analysis yields an intensity pattern for N slits each of width d given by

> where β is the same β as in the single slit diffraction and

> Note that this pattern is comprised of a diffraction envelope together with the (sin2Nγ)/sin2γ term. This latter term leads to the existence of principal maxima predicted by dsinθ = nλ together with much weaker secondary maxima between the principal maxima as shown below for a five slit example.

> ### DIFFRACTION GRATINGS

- The diffraction grating is an important experimental application of the multiple slit maximum/minimum phenomenon. In its simplest form a diffraction grating consistes of a metal or glass plate with many very finely spaced grooves or slits.

- For a metal grating interference occurs in the reflected light. For a glass grating reflected or transmitted light will interfere.

- The "slit" spacing, d, is typically defined by the number of grooves per cm (or inch).

- Principal maxima are located at angles θ given by sinθ = nλ/d. Therefore, the smaller "d" (or the more grooves per cm) the larger the angle θ.

- By examining the exact intensity formula it can be shown that the smaller "d" the brighter the principal maxima are compared to the secondary maxima.

- When an atom is "excited" the spectrum of light it emits de-exciting back to its ground state is characteristic of that particular atom. Thus, observing the spectrum of light emitted by a star gives an accurate measure of the elemental compostion of the star. Since the angle θ depends on the wavelength λ we can use a diffraction grating to obtain the spectrum of the light emitted by the star.

- For a "white" light source a diffraction grating may lead to several "orders", corresponding to n = 1, 2, 3,... Each order will contain the complete spectrum of colors (see below).

> Depending on the value of "d" the various "orders" may overlap. In other words red light (long wavelength) in the first order (n=1) could have the same value of θ as blue light (smaller wavelength) in the second order (n=2).
> Note that in a diffraction grating red light is diffracted through a larger angle than blue light, in contrast to the way in which a prism separates the rainbow of colors (below).

A little boy refused to run anymore. When his mother asked him why, he replied, "I heard that the faster you go, the shorter you become

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu