When waves encounter an obstacle or a narrow opening, they bend and spread out in a phenomenon called diffraction. Imagine water waves passing through a gap in a breakwater; they don’t continue in a straight line but spread in a circular pattern on the other side. This bending is most pronounced when the size of the opening is comparable to the wave’s wavelength. Light, for instance, will diffract when it passes through a very narrow slit, a property that applies to all waves, including sound and electromagnetic radiation.
The Origin of Diffraction Patterns
The creation of a diffraction pattern is explained by Huygens’ principle. This principle states that every point on a wavefront acts as a source of tiny, secondary wavelets spreading forward. When a wave passes through an aperture, a line of these new wavelet sources is effectively created in the opening.
These new wavelets travel outward from the slit and interfere with one another. Constructive interference occurs when the crests of waves align, reinforcing each other to create a bright spot of greater intensity.
Destructive interference happens when the crest of one wave aligns with the trough of another, causing them to cancel each other out and result in a dark spot. The combination of these interference events produces the series of bright and dark fringes known as a diffraction pattern.
Characteristics of Diffraction Minima
The areas of complete darkness in a diffraction pattern are known as diffraction minima, which are locations of perfect destructive interference. At these points, for every wavelet arriving with an upward displacement (a crest), another arrives with an equal downward displacement (a trough). This results in a complete cancellation of their amplitudes, creating a point of zero light intensity observed as a dark band.
These dark fringes are not simply shadows; they are an active result of wave interference. While the bright fringes, or maxima, are where wave energy is concentrated, the minima are the locations where that energy has been nullified. The spacing and width of these minima are determined by the physical properties of the setup, such as the wavelength of the light and the size of the opening it passes through.
Calculating the Location of Minima
The precise angular position of diffraction minima from a single slit is predicted by the formula a sin(θ) = mλ. This equation connects the setup’s geometry to the wave’s properties.
The variables in the formula are:
- a is the width of the slit.
- θ (theta) is the angle from the pattern’s center to a specific minimum.
- λ (lambda) is the wavelength of the light.
- m is the order of the minimum, which is any non-zero integer (e.g., ±1, ±2, ±3).
The integer m cannot be zero, as the position m=0 corresponds to the central bright maximum. This relationship shows that using light with a longer wavelength (a larger λ) or a narrower slit (a smaller a) will cause the minima to spread further apart, widening the pattern.
Minima in Single-Slit vs. Multi-Slit Setups
The appearance of diffraction minima changes in a multi-slit setup, like a double-slit or diffraction grating. The resulting pattern combines two effects: diffraction from each individual slit and interference between the different slits.
The broad shape, or “envelope,” of the pattern is dictated by the diffraction from each slit. The minima of this envelope appear at the same angles as they would for a single slit of the same width. The formula a sin(θ) = mλ still determines the location of these major dark bands.
Within this broad envelope, a more intricate and finely spaced pattern of interference fringes appears. This pattern is caused by interference between the multiple slits. The principle of single-slit minima does not vanish; it defines the larger structure for the more complex multi-slit pattern.