Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - Title Sequence

• Definition of diffraction
• Diffraction patterns
• Single-slit diffraction
• Circular aperture diffraction
• Factors affecting diffraction patterns

Definition of diffraction

• Diffraction is the bending or spreading of waves around obstacles or through openings
• It occurs when waves encounter an obstacle or an opening that is of comparable size to their wavelength
• It results in the spreading out of the wavefront

Diffraction patterns

• Diffraction patterns are the interference patterns formed by waves after they undergo diffraction
• They can be observed when waves pass through a narrow slit or a circular aperture
• They exhibit characteristics such as intensity distribution and interference fringes

Single-slit diffraction

• Single-slit diffraction occurs when waves pass through a narrow slit
• It leads to the formation of a central bright fringe surrounded by alternating dark and bright fringes
• The width of the central fringe is larger compared to the other fringes
• The intensity of the fringes decreases as the distance from the central fringe increases

Circular aperture diffraction

• Circular aperture diffraction occurs when waves pass through a circular opening
• It leads to the formation of a central bright spot surrounded by alternating dark and bright rings
• The central spot is larger compared to the rings and has higher intensity
• The diameter of the rings decreases as the distance from the central spot increases

Factors affecting diffraction patterns

• Wavelength of the waves: Longer wavelengths produce more diffraction
• Size of the aperture or the slit: Smaller apertures or slits produce more diffraction
• Distance from the source to the screen: Greater distances result in narrower fringes or rings
• Size of the source: Smaller sources produce better-defined diffraction patterns

Slide 11: Single-slit diffraction (contd.)

• The position of bright and dark fringes can be calculated using the equation
  • For the mth order fringe: sinθ = mλ / a
    • θ is the angle of diffraction
    • λ is the wavelength of the waves
    • a is the width of the slit
    • m is the order of the fringe

Slide 12: Single-slit diffraction (contd.)

• The intensity of the fringes can be calculated using the equation
  • For the mth order fringe: I = I₀ (sinα / α)²
    • I is the intensity of the fringe
    • I₀ is the intensity at the center of the central fringe
    • α is the angle formed by the midpoint of the slit and the mth order fringe

Slide 13: Circular aperture diffraction

• Unlike single-slit diffraction, circular aperture diffraction produces more complex patterns
• The central spot is known as the Airy disk or central maximum
• The intensity gradually decreases as we move away from the central spot

Slide 14: Circular aperture diffraction (contd.)

• The position of the dark rings can be calculated using the equation
  • For the nth dark ring: r = sqrt(nλL)
    • r is the radius of the dark ring
    • λ is the wavelength of the waves
    • L is the distance from the aperture to the screen

Slide 15: Circular aperture diffraction (contd.)

• The intensity of the rings can be calculated using the equation
  • For the nth order ring: I = I₀J₁²(x) / x²
    • I is the intensity of the ring
    • I₀ is the intensity at the center of the Airy disk
    • J₁(x) is the first-order Bessel function
    • x is the distance from the center of the Airy disk

Slide 16: Factors affecting diffraction patterns (contd.)

• Polarization: The polarization of waves affects the diffraction pattern
• When waves are polarized perpendicular to the slit or aperture, the diffraction pattern may appear different compared to unpolarized waves

Slide 17: Factors affecting diffraction patterns (contd.)

• Distance from the source to the screen: As the distance increases, the diffraction pattern becomes narrower and more well-defined

Slide 18: Factors affecting diffraction patterns (contd.)

• Size of the source: A smaller source produces better-defined diffraction patterns compared to a larger source

Slide 19: Applications of diffraction patterns

• Diffraction patterns are used in various scientific and technological applications, including:
  • X-ray crystallography to determine atomic structures
  • Optical microscopy to enhance resolution
  • Spectroscopy to analyze the properties of materials

Slide 20: Conclusion

• Diffraction patterns occur when waves pass through narrow slits or circular apertures
• Single-slit diffraction produces a central bright fringe surrounded by alternating dark and bright fringes
• Circular aperture diffraction produces a central bright spot surrounded by alternating dark and bright rings
• Various factors such as wavelength, size of the aperture or slit, distance, and source size affect the diffraction patterns

Slide 21: Diffraction grating

• A diffraction grating is an optical device that contains a large number of equally spaced slits or rulings
• It is used to separate light into its component wavelengths
• The spacing between the slits determines the angular separation of the diffracted wavelengths
• The formula for the angular separation is given by: sinθ = mλ / d, where d is the spacing between the slits and m is the order of the maximum

Slide 22: Diffraction and interference

• Diffraction and interference are closely related phenomena
• Diffraction is the bending and spreading of waves around obstacles or through openings
• Interference is the interaction and superposition of waves, resulting in constructive or destructive interference
• Both phenomena can be observed in diffraction patterns

Slide 23: Diffraction in everyday life

• Diffraction is not limited to the study of light waves
• It can also be observed in everyday life, such as:
  • The bending of sound waves around obstacles
  • The spreading of water waves after passing through a small opening
  • The interference patterns formed by radio waves

Slide 24: Diffraction in photography

• Diffraction affects the quality and sharpness of images in photography
• As light passes through a small aperture in a camera lens, it diffracts, leading to a decrease in image sharpness
• This is why larger apertures (smaller f-numbers) are used to capture sharper images with less diffraction

Slide 25: Diffraction-limited resolution

• The diffraction-limited resolution is the maximum resolution that can be achieved for an optical system
• It is determined by the wavelength of light and the size of the aperture
• The formula for the diffraction-limited resolution is given by: θ ≈ 1.22λ / D, where θ is the angular resolution, λ is the wavelength, and D is the diameter of the aperture

Slide 26: Rayleigh criterion

• The Rayleigh criterion is used to determine the minimum resolvable detail in an optical system
• According to the criterion, two point sources are just resolvable if the maximum of the central diffraction pattern of one source coincides with the first minimum of the diffraction pattern of the other source
• The formula for the Rayleigh criterion is given by: θ ≈ 1.22λ / D, where θ is the angular resolution, λ is the wavelength, and D is the diameter of the aperture

Slide 27: Applications of diffraction

• Diffraction has numerous applications in various fields, including:
  • X-ray diffraction for studying crystal structures
  • Spectrophotometry for analyzing the chemical composition of substances
  • Holography for creating three-dimensional images
  • Optical storage devices such as CDs and DVDs

Slide 28: Diffraction in astronomy

• Diffraction plays a crucial role in astronomy, allowing scientists to study distant celestial objects and phenomena
• Astronomers use various diffraction-based techniques, such as:
  • Spectroscopy to analyze the composition and temperature of stars
  • Interferometry to enhance resolution and study distant objects
  • Coronagraphy to observe the faint structures around stars

Slide 29: Diffraction and wave-particle duality

• Diffraction and interference phenomena provide evidence for the wave nature of particles such as electrons and photons
• The diffraction of electrons and photons, observed in experiments, supports the concept of wave-particle duality
• The diffraction patterns obtained are consistent with the wave nature of particles

Slide 30: Summary

• Diffraction is the bending and spreading of waves around obstacles or through openings
• Diffraction patterns can be observed when waves pass through narrow slits or circular apertures
• The properties of the diffraction pattern depend on factors such as wavelength, size of the aperture or slit, and distance between the source and the screen
• Diffraction has applications in various fields, including optics, spectroscopy, astronomy, and particle physics