27.3 Young’s Double Slit Experiment

Young's double slit experiment reveals light's wave nature through interference patterns. When light passes through two slits, it creates alternating bright and dark fringes on a screen, demonstrating constructive and destructive interference.

The experiment's results depend on wavelength, slit separation, and screen distance. It showcases superposition, where waves combine to form a resultant wave, and provides evidence for light's wave-particle duality.

Young's Double Slit Experiment

Young's double slit interference pattern

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• Interference pattern consists of alternating bright and dark fringes on a screen
  • Bright fringes are areas of constructive interference where waves from the two slits arrive in phase, reinforcing each other (light waves)
  • Dark fringes are areas of destructive interference where waves from the two slits arrive out of phase, canceling each other (sound waves)
• Central bright fringe is the brightest and widest as it is equidistant from both slits, resulting in maximum constructive interference (laser light)
• Bright fringes become dimmer and narrower moving away from the center because the path length difference increases, reducing the degree of constructive interference (water waves)
• Spacing between fringes depends on the wavelength of light and the distance between the slits
  • Larger wavelengths (red light) or smaller slit separations result in wider fringe spacing
  • Smaller wavelengths (blue light) or larger slit separations lead to narrower fringe spacing
• The experiment demonstrates the principle of superposition, where waves combine to produce a resultant wave

Angles of constructive vs destructive interference

• Constructive interference occurs when the path length difference is an integer multiple of the wavelength
  • $d \sin \theta = [m](https://www.fiveableKeyTerm:m) \lambda$, where $d$ is the slit separation, $\theta$ is the angle, $m$ is an integer (0, ±1, ±2, ...), and $\lambda$ is the wavelength
• Destructive interference occurs when the path length difference is a half-integer multiple of the wavelength
  • $d \sin \theta = (m + \frac{1}{2}) \lambda$, where $m$ is an integer (0, ±1, ±2, ...)
• To calculate the angles:
  1. Solve the equation for $\theta$ using the given slit separation ($d$) and wavelength ($\lambda$)
  2. For constructive interference, use integer values of $m$ (0, ±1, ±2, ...)
  3. For destructive interference, use half-integer values of $m$ (±0.5, ±1.5, ±2.5, ...)

Path length difference in interference

• Path length difference determines the phase relationship between waves arriving at a point on the screen
  • When the path length difference is an integer multiple of the wavelength, waves arrive in phase, causing constructive interference and resulting in a bright fringe (crest meeting crest)
  • When the path length difference is a half-integer multiple of the wavelength, waves arrive out of phase, causing destructive interference and resulting in a dark fringe (crest meeting trough)
• As the angle from the central axis increases, the path length difference between the waves from the two slits also increases, leading to alternating regions of constructive and destructive interference (angular dependence)
• The degree of constructive or destructive interference depends on the exact path length difference
  • Maximum constructive interference occurs when the path length difference is exactly an integer multiple of the wavelength (complete reinforcement)
  • Partial constructive or destructive interference occurs for path length differences between integer and half-integer multiples of the wavelength (partial reinforcement or cancellation)

Wave properties and experimental setup

• The experiment requires coherent light to produce a clear interference pattern
• Diffraction occurs as light passes through the narrow slits, causing the waves to spread out
• The double-slit interferometer is the experimental apparatus used to observe the interference pattern
• Young's experiment provides evidence for the wave-particle duality of light, showing both wave-like interference and particle-like behavior