Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - The Airy Pattern’
- In this lecture, we will discuss the diffraction patterns that are formed due to a single-slit and a circular aperture.
- Diffraction is the bending of waves around obstacles or through small openings.
- The phenomenon of diffraction plays a significant role in understanding the behavior of light waves.
- Diffraction patterns can be observed when light waves pass through a single slit or a circular aperture.
- These patterns are known as the Airy patterns and have distinct characteristics.
Diffraction Patterns Due to a Single-Slit
- When light from a source passes through a narrow single-slit aperture, it diffracts and forms a diffraction pattern.
- The pattern consists of a central bright maximum, known as the principal maximum, surrounded by alternating dark and bright fringes.
- The central maximum is more intense and wider than the other fringes.
- The size and number of fringes depend on the width of the slit and the wavelength of light.
- The narrower the slit, the more pronounced the diffraction effects.
Diffraction Patterns Due to a Single-Slit (Contd.)
- The angular position of the first-order minimum (dark fringe) can be calculated using the formula:
θ = λ / b
where θ is the angle of diffraction, λ is the wavelength of light, and b is the width of the slit.
- The angular position of the second-order minimum can be calculated using the formula:
sin θ = (2n + 1) λ / b
where n is the order of the minimum.
Diffraction Patterns Due to a Single-Slit (Contd.)
- It is important to note that as the order of the minimum increases, the intensity of the fringes decreases.
- The central maximum is always the brightest part of the diffraction pattern.
- The overall shape of the diffraction pattern resembles a single-slit interference pattern but with much lower fringe intensity.
Diffraction Patterns Due to a Circular Aperture
- When light passes through a circular aperture, it forms a diffraction pattern known as the Airy pattern.
- The Airy pattern consists of a bright central region known as the Airy disk, surrounded by concentric dark and bright rings.
- The Airy pattern is characteristic of diffraction caused by a circular aperture and can be observed in various optical systems.
- The diameter of the Airy disk and the spacing between the rings depend on the size of the aperture and the wavelength of light.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The angular radius of the central bright disk (θ) can be approximated using the formula:
θ ≈ 1.22 λ / D
where θ is the angular radius, λ is the wavelength of light, and D is the diameter of the aperture.
- The angular radius determines the size of the Airy disk, with smaller values indicating sharper resolution.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The spacing between the dark rings and bright rings of the Airy pattern can be approximated using the formula:
θ ≈ m λ / D
where θ is the angular radius, λ is the wavelength of light, D is the diameter of the aperture, and m is the order of the ring.
- As the order of the ring increases, the intensity of the fringes decreases, similar to the diffraction pattern due to a single-slit.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The Airy pattern is important in astronomy and microscopy as it determines the resolution of optical instruments.
- Instruments with large apertures and small wavelengths of light can achieve higher resolutions and better image quality.
- Diffraction can limit the sharpness of images produced by optical instruments, making it a crucial consideration in their design and usage.
Example: Diffraction Pattern Calculations
- Let’s consider an example where monochromatic light with a wavelength of 600 nm passes through a single-slit aperture with a width of 0.01 mm.
- Calculate the angular position of the first-order minimum.
- Solution:
- Given:
- λ = 600 nm = 6 × 10^(-7) m
- b = 0.01 mm = 0.01 × 10^(-3) m
- Using the formula:
- θ = λ / b
- θ = 6 × 10^(-7) / 0.01 × 10^(-3)
- θ ≈ 0.06 radians
Example: Diffraction Pattern Calculations (Contd.)
- Let’s continue the example and calculate the angular position of the third-order minimum.
- Solution:
- Given:
- m = 3
- b = 0.01 mm = 0.01 × 10^(-3) m
- λ = 600 nm = 6 × 10^(-7) m
- Using the formula:
- sin θ = (2n + 1) λ / b
- sin θ = (2 × 3 + 1) × 6 × 10^(-7) / (0.01 × 10^(-3))
- sin θ ≈ 1.2 × 10^(-2)
- θ ≈ 1.2 × 10^(-2) radians.
Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - The Airy Pattern’
- In this lecture, we will discuss the diffraction patterns that are formed due to a single-slit and a circular aperture.
- Diffraction is the bending of waves around obstacles or through small openings.
- The phenomenon of diffraction plays a significant role in understanding the behavior of light waves.
- Diffraction patterns can be observed when light waves pass through a single slit or a circular aperture.
- These patterns are known as the Airy patterns and have distinct characteristics.
Diffraction Patterns Due to a Single-Slit
- When light from a source passes through a narrow single-slit aperture, it diffracts and forms a diffraction pattern.
- The pattern consists of a central bright maximum, known as the principal maximum, surrounded by alternating dark and bright fringes.
- The central maximum is more intense and wider than the other fringes.
- The size and number of fringes depend on the width of the slit and the wavelength of light.
- The narrower the slit, the more pronounced the diffraction effects.
Diffraction Patterns Due to a Single-Slit (Contd.)
- The angular position of the first-order minimum (dark fringe) can be calculated using the formula:
θ = λ / b
where θ is the angle of diffraction, λ is the wavelength of light, and b is the width of the slit.
- The angular position of the second-order minimum can be calculated using the formula:
sin θ = (2n + 1) λ / b
where n is the order of the minimum.
Diffraction Patterns Due to a Single-Slit (Contd.)
- It is important to note that as the order of the minimum increases, the intensity of the fringes decreases.
- The central maximum is always the brightest part of the diffraction pattern.
- The overall shape of the diffraction pattern resembles a single-slit interference pattern but with much lower fringe intensity.
Diffraction Patterns Due to a Circular Aperture
- When light passes through a circular aperture, it forms a diffraction pattern known as the Airy pattern.
- The Airy pattern consists of a bright central region known as the Airy disk, surrounded by concentric dark and bright rings.
- The Airy pattern is characteristic of diffraction caused by a circular aperture and can be observed in various optical systems.
- The diameter of the Airy disk and the spacing between the rings depend on the size of the aperture and the wavelength of light.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The angular radius of the central bright disk (θ) can be approximated using the formula:
θ ≈ 1.22 λ / D
where θ is the angular radius, λ is the wavelength of light, and D is the diameter of the aperture.
- The angular radius determines the size of the Airy disk, with smaller values indicating sharper resolution.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The spacing between the dark rings and bright rings of the Airy pattern can be approximated using the formula:
θ ≈ m λ / D
where θ is the angular radius, λ is the wavelength of light, D is the diameter of the aperture, and m is the order of the ring.
- As the order of the ring increases, the intensity of the fringes decreases, similar to the diffraction pattern due to a single-slit.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The Airy pattern is important in astronomy and microscopy as it determines the resolution of optical instruments.
- Instruments with large apertures and small wavelengths of light can achieve higher resolutions and better image quality.
- Diffraction can limit the sharpness of images produced by optical instruments, making it a crucial consideration in their design and usage.
Example: Diffraction Pattern Calculations
- Let’s consider an example where monochromatic light with a wavelength of 600 nm passes through a single-slit aperture with a width of 0.01 mm.
- Calculate the angular position of the first-order minimum.
- Solution:
- Given:
- λ = 600 nm = 6 × 10^(-7) m
- b = 0.01 mm = 0.01 × 10^(-3) m
- Using the formula:
- θ = λ / b
- θ = 6 × 10^(-7) / 0.01 × 10^(-3)
- θ ≈ 0.06 radians
Example: Diffraction Pattern Calculations (Contd.)
- Let’s continue the example and calculate the angular position of the third-order minimum.
- Solution:
- Given:
- m = 3
- b = 0.01 mm = 0.01 × 10^(-3) m
- λ = 600 nm = 6 × 10^(-7) m
- Using the formula:
- sin θ = (2n + 1) λ / b
- sin θ = (2 × 3 + 1) × 6 × 10^(-7) / (0.01 × 10^(-3))
- sin θ ≈ 1.2 × 10^(-2)
- θ ≈ 1.2 × 10^(-2) radians.
Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - The Airy Pattern'
- Diffraction is the bending of waves around obstacles or through small openings.
- It is an important phenomenon in the study of light waves.
- In this lecture, we will discuss diffraction patterns formed due to a single-slit and a circular aperture.
- These patterns are known as the Airy patterns.
- The Airy pattern due to a single-slit consists of a central bright maximum surrounded by alternating dark and bright fringes.
- The Airy pattern due to a circular aperture consists of a bright central region (Airy disk) surrounded by concentric dark and bright rings.
Diffraction Patterns Due to a Single-Slit
- When light passes through a narrow single-slit aperture, it diffracts and forms a distinctive pattern.
- The diffraction pattern consists of a central bright maximum, also known as the principal maximum.
- The principal maximum is wider and more intense compared to the other fringes.
- Surrounding the principal maximum are alternating dark and bright fringes.
- The intensity of the fringes decreases as the order of the fringe increases.
Diffraction Patterns Due to a Single-Slit (Contd.)
- The angular position of the first-order minimum (dark fringe) can be calculated using the formula:
θ = λ / b
where θ is the angle of diffraction, λ is the wavelength of light, and b is the width of the slit.
- The angular position of the second-order minimum can be calculated using the formula:
sin θ = (2n + 1) λ / b
where n is the order of the minimum.
Diffraction Patterns Due to a Single-Slit (Contd.)
- The intensity of the fringes decreases as the order of the fringe increases.
- The central maximum is always the most intense part of the diffraction pattern.
- The overall shape of the diffraction pattern resembles a single-slit interference pattern but with lower fringe intensity.
- The width of the slit plays a significant role in determining the size and number of fringes.
Diffraction Patterns Due to a Circular Aperture
- When light passes through a circular aperture, it forms a characteristic diffraction pattern known as the Airy pattern.
- The Airy pattern consists of a bright central region called the Airy disk.
- Surrounding the Airy disk are concentric rings, with alternating dark and bright regions.
- The diameter of the Airy disk and the spacing between the rings depend on the size of the aperture and the wavelength of light.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The angular radius of the central bright disk (θ) can be approximated using the formula:
θ ≈ 1.22 λ / D
where θ is the angular radius, λ is the wavelength of light, and D is the diameter of the aperture.
- The angular radius determines the size of the Airy disk, with smaller values indicating sharper resolution.
- A larger aperture diameter leads to a smaller angular radius and improves resolution.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The spacing between the dark rings and bright rings of the Airy pattern can be approximated using the formula:
θ ≈ m λ / D
where θ is the angular radius, λ is the wavelength of light, D is the diameter of the aperture, and m is the order of the ring.
- As the order of the ring increases, the intensity of the fringes decreases.
- The diffraction pattern due to a circular aperture is similar to the one produced by a single-slit, with alternating dark and bright regions.
Diffraction Patterns Due to a Circular Aperture (Contd.)
- The Airy pattern is crucial in various fields, including astronomy and microscopy.
- The resolution of optical instruments depends on the Airy pattern.
- Instruments with larger apertures and smaller wavelengths of light can achieve higher resolution and better image quality.
- Diffraction can limit the sharpness of images produced by optical instruments and must be considered during design and usage.
Example: Diffraction Pattern Calculations
- Consider monochromatic light with a wavelength of 600 nm passing through a single-slit aperture with a width of 0.01 mm.
- Calculate the angular position of the first-order minimum.
- Solution:
- Given:
- λ = 600 nm = 6 × 10^(-7) m
- b = 0.01 mm = 0.01 × 10^(-3) m
- Using the formula:
- θ = λ / b
- θ = 6 × 10^(-7) / 0.01 × 10^(-3)
- θ ≈ 0.06 radians
Example: Diffraction Pattern Calculations (Contd.)
- Let’s continue the example and calculate the angular position of the third-order minimum.
- Solution:
- Given:
- m = 3
- b = 0.01 mm = 0.01 × 10^(-3) m
- λ = 600 nm = 6 × 10^(-7) m
- Using the formula:
- sin θ = (2n + 1) λ / b
- sin θ = (2 × 3 + 1) × 6 × 10^(-7) / (0.01 × 10^(-3))
- sin θ ≈ 1.2 × 10^(-2)
- θ ≈ 1.2 × 10^(-2) radians.