Diffraction - Destructive Interference

Introduction

• Destructive interference is a phenomenon that occurs when two waves overlap and their amplitudes cancel each other out, resulting in a weaker or darker region.

Conditions for Destructive Interference

• Destructive interference happens when waves from two sources, denoted as A and B, arrive at a point out of phase with each other.
• This means that the crests of wave A coincide with the troughs of wave B, and vice versa.

Path Difference

• To achieve destructive interference, the path difference (the difference in the distances traveled by the waves) from source A and source B to the point of interest must be an odd multiple of half of the wavelength (λ/2) of the waves.
• The path difference can be expressed as: Δx = (2n + 1) (λ/2)
• Where:
  • Δx is the path difference.
  • n is an integer (0, 1, 2, 3, ...).
  • λ is the wavelength of the waves.

Visualizing Destructive Interference

• In practical terms, this means that the crests of one wave overlap with the troughs of the other wave, leading to a reduction or cancellation of amplitude.
• For example, if n = 0, it indicates that there is no path difference, and the waves overlap perfectly but out of phase, resulting in destructive interference.

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Diffraction - Destructive Interference

Applications

• Destructive interference is observed in various wave phenomena, including light and sound.
• In optics, it creates dark fringes or regions with reduced brightness in interference patterns, such as those seen in the double-slit experiment.
• In acoustics, it leads to reduced or cancelled sound amplitudes when waves overlap destructively.