Light behaves like a wave, bending around obstacles and creating patterns when it passes through openings. This wave-like nature explains diffraction and interference, key phenomena that occur when light interacts with its environment.

Understanding light's wave behavior helps us measure its wavelength and predict how it will spread out. We can use equations and principles like Huygens's to explain these effects and apply them in various optical systems.

Wave Behavior of Light

Wave behavior of light

• Light exhibits wave-like properties such as diffraction and interference
• Diffraction occurs when waves bend around obstacles or pass through openings
  • Single-slit diffraction happens when light passes through a narrow slit, spreading out and forming a diffraction pattern with a wide central bright fringe and dark fringes on either side
  • Double-slit diffraction occurs when light passes through two parallel slits, forming an interference pattern with alternating bright and dark fringes on a screen
• Interference is the superposition of waves from multiple sources
  • Constructive interference happens when waves are in phase and their amplitudes add, creating bright fringes in the double-slit experiment
  • Destructive interference occurs when waves are out of phase and their amplitudes cancel, resulting in dark fringes in the double-slit experiment
• Wave superposition occurs when multiple waves combine, leading to interference patterns

Wavelength calculation from interference

• The wavelength of light can be calculated using the double-slit interference equation: $\lambda = \frac{xd}{mL}$
  • $\lambda$ represents the wavelength of light
  • $x$ is the distance between the central bright fringe and the $m^{th}$ bright fringe
  • $d$ denotes the separation between the two slits
  • $m$ is the order of the bright fringe (central fringe has $m=0$)
  • $L$ represents the distance between the slits and the screen
• To calculate the wavelength:
  1. Measure the distance $x$ between the central bright fringe and a higher-order bright fringe
  2. Determine the order $m$ of the chosen bright fringe
  3. Measure the separation $d$ between the two slits
  4. Measure the distance $L$ between the slits and the screen
  5. Substitute the measured values into the equation and solve for $\lambda$
• Young's double-slit experiment demonstrates interference and is used to measure the wavelength of light

Huygens's principle for wavefronts

• Huygens's principle states that every point on a wavefront acts as a source of secondary wavelets that spread out in all directions
• The wavefront at any later time is the envelope of these secondary wavelets
• This principle explains the propagation of waves and their behavior when encountering obstacles or openings
• Diffraction of light through openings can be understood using Huygens's principle
  • Each point on the wavefront at the opening acts as a source of secondary wavelets that spread out and interfere with each other
  • The resulting diffraction pattern depends on the size and shape of the opening relative to the wavelength of light (smaller openings lead to more pronounced diffraction, while larger openings result in less noticeable diffraction)
• Huygens's principle helps explain the formation of diffraction patterns in single-slit and double-slit experiments
  • In single-slit experiments, secondary wavelets from the slit interfere, creating the single-slit diffraction pattern
  • In double-slit experiments, secondary wavelets from each slit interfere, resulting in the double-slit interference pattern

Advanced Diffraction Concepts

• Fraunhofer diffraction occurs when the light source and observation point are effectively at infinity, resulting in parallel wavefronts
• Diffraction gratings consist of multiple parallel slits or grooves, producing complex interference patterns
• Coherence is the degree of correlation between the phases of waves, affecting their ability to produce stable interference patterns
• Phase difference between waves determines the type of interference (constructive or destructive) that occurs when they combine