• Diffraction is the bending or spreading of waves when they encounter an obstacle or pass through an aperture

    • It is observed in various wave phenomena, such as light, sound, and water waves
  • Today, we will discuss “Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture'”

  • Single-slit diffraction:

    • When light passes through a narrow slit, it diffracts and creates a pattern of bright and dark bands on a screen
    • The central bright band is the widest, and each subsequent band is narrower and less intense
    • The pattern is characterized by the central maximum and secondary maxima and minima
  • Single-slit diffraction equation:

    • For a single-slit of width ‘a’, the angle at which the first minimum is formed is given by:
    • sinθ = λ / a
      • θ: angle between the line perpendicular to the slit and the first minimum
      • λ: wavelength of light used
      • a: width of the slit
  • Circular aperture diffraction:

    • When light passes through a circular aperture, it produces a diffraction pattern with concentric bright and dark rings
    • The central bright spot is called the Airy disk, and subsequent rings are less intense
    • The pattern is characterized by the central maximum and rings of decreasing intensity
  • Circular aperture diffraction equation:

    • The angle at which the first minimum is formed can be determined using the equation:
    • sinθ = 1.22 * λ / D
      • θ: angle between the line perpendicular to the aperture and the first minimum
      • λ: wavelength of light used
      • D: diameter of the aperture
  • Intensity function in double-slit experiment (with slit of finite width):

    • In the double-slit experiment, when the slits have a finite width, the intensity at a point in the interference pattern depends on the superposition of waves diffracted from each slit
    • The intensity at a point on the screen can be calculated using the intensity function:
    • I = I₁ + I₂ + 2√(I₁ * I₂) * cos(δ)
      • I₁ and I₂: intensities of light from each slit individually
      • δ: phase difference between the waves from each slit
  • Diffraction patterns can be seen in various natural phenomena and applications:

    • Rainbows, where sunlight undergoes diffraction and dispersion
    • Sunsets, where the Sun’s light is scattered and diffracted as it passes through the Earth’s atmosphere
    • CD or DVD discs, where diffraction patterns are encoded to store information
    • Microscopic imaging techniques, such as diffraction-limited microscopy, utilize diffraction patterns to enhance resolution
  • Examples of diffraction patterns:

    • The diffraction grating, consisting of parallel slits, produces a pattern of multiple order maxima and minima
    • X-ray crystallography uses the diffraction pattern generated by x-rays passing through a crystal to determine its atomic structure
    • Ultrasonic waves diffracting around obstacles or through narrow openings produce characteristic diffraction patterns
  • Applications of diffraction in everyday life:

    • The principle of diffraction is applied in the design of audio speakers, which use diffraction to disperse sound waves evenly
    • Diffraction gratings are used in spectrophotometers and monochromators for precise wavelength selection and analysis of light
    • Holography relies on the interference and diffraction of light to create three-dimensional images
  • In conclusion:

    • Diffraction is an important wave phenomenon observed in various fields, including optics, acoustics, and water waves
    • Single-slit diffraction and circular aperture diffraction produce characteristic patterns of bright and dark regions
    • The intensity at a point in a double-slit experiment with finite slit width is determined by the interference and diffraction of waves
    • Diffraction patterns have practical applications in technology and are widely observed in nature Sure! Here are slides 11 to 20:
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Diffraction is the bending or spreading of waves when they encounter an obstacle or pass through an aperture It is observed in various wave phenomena, such as light, sound, and water waves Today, we will discuss “Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture'” Single-slit diffraction: When light passes through a narrow slit, it diffracts and creates a pattern of bright and dark bands on a screen The central bright band is the widest, and each subsequent band is narrower and less intense The pattern is characterized by the central maximum and secondary maxima and minima Single-slit diffraction equation: For a single-slit of width ‘a’, the angle at which the first minimum is formed is given by: sinθ = λ / a θ: angle between the line perpendicular to the slit and the first minimum λ: wavelength of light used a: width of the slit Circular aperture diffraction: When light passes through a circular aperture, it produces a diffraction pattern with concentric bright and dark rings The central bright spot is called the Airy disk, and subsequent rings are less intense The pattern is characterized by the central maximum and rings of decreasing intensity Circular aperture diffraction equation: The angle at which the first minimum is formed can be determined using the equation: sinθ = 1.22 * λ / D θ: angle between the line perpendicular to the aperture and the first minimum λ: wavelength of light used D: diameter of the aperture Intensity function in double-slit experiment (with slit of finite width): In the double-slit experiment, when the slits have a finite width, the intensity at a point in the interference pattern depends on the superposition of waves diffracted from each slit The intensity at a point on the screen can be calculated using the intensity function: I = I₁ + I₂ + 2√(I₁ * I₂) * cos(δ) I₁ and I₂: intensities of light from each slit individually δ: phase difference between the waves from each slit Diffraction patterns can be seen in various natural phenomena and applications: Rainbows, where sunlight undergoes diffraction and dispersion Sunsets, where the Sun’s light is scattered and diffracted as it passes through the Earth’s atmosphere CD or DVD discs, where diffraction patterns are encoded to store information Microscopic imaging techniques, such as diffraction-limited microscopy, utilize diffraction patterns to enhance resolution Examples of diffraction patterns: The diffraction grating, consisting of parallel slits, produces a pattern of multiple order maxima and minima X-ray crystallography uses the diffraction pattern generated by x-rays passing through a crystal to determine its atomic structure Ultrasonic waves diffracting around obstacles or through narrow openings produce characteristic diffraction patterns Applications of diffraction in everyday life: The principle of diffraction is applied in the design of audio speakers, which use diffraction to disperse sound waves evenly Diffraction gratings are used in spectrophotometers and monochromators for precise wavelength selection and analysis of light Holography relies on the interference and diffraction of light to create three-dimensional images In conclusion: Diffraction is an important wave phenomenon observed in various fields, including optics, acoustics, and water waves Single-slit diffraction and circular aperture diffraction produce characteristic patterns of bright and dark regions The intensity at a point in a double-slit experiment with finite slit width is determined by the interference and diffraction of waves Diffraction patterns have practical applications in technology and are widely observed in nature Sure! Here are slides 11 to 20: