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:
Slide 11:
Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - Intensity function in double-slit experiment (with slit of finite width)’
In a 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)
Here, I₁ and I₂ are the intensities of light from each slit individually, and δ is the phase difference between the waves from each slit
Slide 12:
Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - Intensity function in double-slit experiment (with slit of finite width)'
The intensity function equation shows that the interference pattern is modified by the diffraction of light at the slits
The term 2√(I₁ * I₂) * cos(δ) represents the interference fringes resulting from the superposition of waves
Slide 13:
Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - Intensity function in double-slit experiment (with slit of finite width)'
When the phase difference δ is zero or a multiple of 2π, the waves from each slit are in phase, resulting in constructive interference and a bright fringe
When the phase difference δ is an odd multiple of π, the waves from each slit are out of phase, resulting in destructive interference and a dark fringe
Slide 14:
Examples of diffraction and interference patterns:
Interference fringes in soap bubbles, where light is reflected and undergoes constructive and destructive interference
Interference patterns in thin films, such as oil slicks, where light reflects at different layers and interferes
Interference patterns in Newton’s rings, where light is reflected between a glass and a lens, creating concentric bright and dark rings
Slide 15:
Examples of diffraction and interference patterns:
The phenomenon of moiré patterns, where two similar patterns overlap and create a new, distinct pattern
The rings observed when laser light is scattered by small particles, known as Mie scattering, which result from the interference and diffraction of light waves
Slide 16:
Applications of diffraction in technology:
CD or DVD discs use diffraction patterns encoded onto the surface to store and read data
Diffraction gratings are used in spectrophotometers to separate light into its different component wavelengths for analysis
Slide 17:
Applications of diffraction in technology:
X-ray crystallography uses the diffraction pattern generated by x-rays passing through a crystal to determine its atomic structure
Diffraction patterns are used in various microscopy techniques, such as electron microscopy and X-ray microscopy, to enhance resolution and visualize small-scale structures
Slide 18:
Applications of diffraction in nature:
Rainbows are formed when sunlight refracts, reflects, and undergoes diffraction and dispersion in water droplets
Sunsets exhibit diffraction and scattering of sunlight as it passes through the Earth’s atmosphere, resulting in vibrant and colorful skies
Slide 19:
Applications of diffraction in nature:
The diffraction of sound waves around obstacles or through narrow openings can create acoustic shadows or diffraction patterns, which are utilized in noise reduction and sound engineering techniques
Diffraction of water waves around piers, breakwaters, and islands can result in wave patterns and interference effects
Slide 20:
Summary of key points:
The intensity in a double-slit experiment with finite slit width can be calculated using the intensity function
The intensity function incorporates both interference and diffraction effects
Diffraction and interference patterns are observed in various natural phenomena, such as rainbows and sunsets, as well as in technological applications like CD and DVD discs, spectrophotometers, and microscopy techniques
Slide 21:
Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture - Summary'
Diffraction is the bending or spreading of waves when they encounter an obstacle or pass through an aperture
Single-slit diffraction produces a pattern of bright and dark bands, with the central maximum being the widest and subsequent bands narrowing
Circular aperture diffraction creates concentric bright and dark rings, with the central spot known as the Airy disk
Slide 22:
Diffraction Patterns Due to a ‘Single-Slit’ - Factors affecting the pattern:
Wavelength of light: Shorter wavelengths produce narrower diffraction patterns
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: