Double-Slit Interference and Diffraction Gratings
Describe the behavior of a wave and the diffraction pattern resulting from the wave passing through multiple openings.
- The pattern resulting from monochromatic light of wavelength λ incident on two slits a distance d apart is caused by a combination of wave diffraction and wave interference.
- When only considering wave interference, a double slit creates a pattern of uniformly spaced maxima.
- Constructive and destructive interference of the wavefronts originating from each slit will result in bright and dark bands on the screen.
- The amount of interference between two wavefronts depends on the path length difference ΔD of the wavefronts.
- The path length difference ΔD can be described in terms of the slit separation d and the angle θ between the direction of propagation of the wavefront and the normal to the opening by the equation:
- For small angles, where θ < 10°, the small angle approximation can be used to relate λ, d and L to ymax, the distance from the middle of the central bright fringe to the mth order of maximum brightness on the screen. Relevant equation:
- When considering wave interference and wave diffraction, a double slit creates an interference pattern of maxima and minima superimposed within the envelope created by single-slit diffraction.
- Interference patterns produced by light interacting with a double slit indicate that light has wave properties. The source of this discovery was Young’s double-slit experiment.
- Visual representations of double-slit diffraction patterns are useful in determining the physical properties of the slits and the interacting waves.
- A diffraction grating is a collection of evenly spaced parallel slits or openings that produce an interference pattern that is the combination of numerous diffraction patterns superimposed on each other.
- When white light is incident on a diffraction grating, the center maximum is white and the higher-order maxima disperse white light into a rainbow of colors, with the longest-wavelength light (red) appearing farthest from the central maximum.