Diffraction - Geometric Shadow Of Obstacle

Diffraction - Geometric shadow of obstacle

Diffraction of light
Limitations of the geometric shadow of an obstacle
Behavior of light waves
Explanation of diffraction using Huygens’ principle
Interference patterns in diffraction

Diffraction - Geometric shadow of obstacle

Diffraction phenomenon observed when light waves encounter obstacles or openings
Geometric shadow of an obstacle only limited to the region immediately behind it
Light waves spread out and bend around the edges of the obstacle or opening
Diffraction patterns have characteristic dark and bright regions
Diffraction gratings demonstrate interference patterns in diffraction

Huygens’ Principle

Huygens’ principle explains the behavior of light waves during diffraction
Each point on a wavefront acts as a source of secondary spherical waves
The secondary waves interfere with each other, resulting in wavefront distortion
The new wavefront follows the envelope of the secondary wavelets
Explains the bending of light waves around obstacles or openings

Diffraction Patterns

Diffraction patterns exhibit constructive and destructive interference
Bright regions (maxima) occur where constructive interference amplifies the wave
Dark regions (minima) occur where destructive interference cancels out the wave
The pattern depends on the shape of the obstacle, wavelength of the light, and size of the opening
Diffraction is a property of all waves, not just light (sound, water waves, etc.)

Diffraction of Single Slit

When a narrow slit is illuminated with monochromatic light, it produces a diffraction pattern
Central bright region with alternating dark and bright regions on either side
The central bright region is wider and more intense
The dark regions result from destructive interference
The width of the central bright region depends on the width of the slit

Diffraction of Single Slit - Equation

The diffraction pattern of a single slit can be described by the equation:
- wλ = asinθ
- w: Width of the slit
- λ: Wavelength of the incident light
- a: Distance between the screen and the slit
- θ: Angle of diffraction

Diffraction of Single Slit - Example

Consider a single slit of width 0.02 mm
Incident light has a wavelength of 600 nm
The screen is placed 2 m away from the slit
Calculate the angular width of the central bright region Solution: wλ = asinθ

0.02 × 10^-3 m × 600 × 10^-9 m = 2 m × sinθ sinθ = (0.02 × 10^-3 × 600 × 10^-9)/(2) θ = sin^(-1)((0.02 × 10^-3 × 600 × 10^-9)/(2)) θ ≈ 0.48°

Diffraction of Double Slit

When two narrow slits are illuminated with monochromatic light, they produce a pattern of bright and dark regions
Similar to single slit diffraction, but with additional interference between the waves from each slit
The bright regions are narrower and more intense compared to single slit diffraction
The pattern exhibits a central maximum and alternating bright and dark regions on either side

Diffraction of Double Slit - Equation

The diffraction pattern of a double slit can be described by the equation:
- mλ = d sinθ
- m: Order of the bright region (0 for central maximum, ±1 for first-order, ±2 for second-order, etc.)
- λ: Wavelength of the incident light
- d: Distance between the two slits
- θ: Angle of diffraction

Diffraction of Double Slit - Example

Consider a double slit with a separation of 0.1 mm
Incident light has a wavelength of 500 nm
Calculate the angle of the first-order bright region Solution: mλ = d sinθ

1 × 500 × 10^-9 m = 0.1 × 10^-3 m × sinθ sinθ = (1 × 500 × 10^-9)/(0.1 × 10^-3) θ = sin^(-1)((1 × 500 × 10^-9)/(0.1 × 10^-3)) θ ≈ 2.86° Sure! Here are slides 11 to 20 on the topic “Diffraction - Geometric shadow of obstacle”:

Diffraction of light occurs when light waves encounter obstacles or openings
Geometric shadow of an obstacle is limited to the region immediately behind it
Diffraction occurs when light waves spread out and bend around the edges of the obstacle or opening
Diffraction patterns have characteristic dark and bright regions
Diffraction can be observed in various situations, such as the spreading of light through a narrow slit

The geometric shadow of an obstacle is based on the assumption that light travels in straight lines
However, light also behaves as a wave and exhibits diffraction effects
Diffraction is a property of all waves, not just light
Sound waves, water waves, and other types of waves also experience diffraction
The study of diffraction helps explain various phenomena, including interference patterns

Huygens’ principle explains the behavior of light waves during diffraction
According to Huygens’ principle, each point on a wavefront acts as a source of secondary spherical waves
These secondary waves interfere with each other, resulting in wavefront distortion
The new wavefront follows the envelope of the secondary wavelets
Huygens’ principle provides a theoretical framework to understand diffraction

Diffraction patterns exhibit both constructive and destructive interference
Constructive interference occurs when wave crests align and reinforce each other, resulting in bright regions
Destructive interference occurs when wave crests and troughs cancel each other out, resulting in dark regions
The pattern of dark and bright regions depends on various factors like the shape and size of the obstacle or opening
The wavelength of the incident light also affects the diffraction pattern

The diffraction pattern of a single slit can be described by the equation: wλ = asinθ
w is the width of the slit, λ is the wavelength of the incident light, a is the distance between the slit and the screen, and θ is the angle of diffraction
The width of the central bright region in the diffraction pattern depends on the width of the slit
As the slit width decreases, the central bright region becomes narrower and more intense
The diffraction of light through a single slit is a fundamental concept in understanding diffraction phenomena

Example:
- Consider a single slit of width 0.02 mm
- Incident light has a wavelength of 600 nm
- The screen is placed 2 m away from the slit
- Calculate the angular width of the central bright region
- Solution: wλ = asinθ
- Substitute the given values: 0.02 × 10^-3 m × 600 × 10^-9 m = 2 m × sinθ
- Solve for θ: sinθ ≈ (0.02 × 10^-3 × 600 × 10^-9)/(2)
- Calculate θ: θ ≈ 0.48°

The diffraction pattern of a double slit can be described by the equation: mλ = d sinθ
m represents the order of the bright region (0 for the central maximum, ±1 for the first-order, ±2 for the second-order, etc.)
λ is the wavelength of the incident light, d is the distance between the two slits, and θ is the angle of diffraction
The double slit diffraction pattern exhibits a central maximum and alternating bright and dark regions
The bright regions become narrower and more intense as the order increases

Example:
- Consider a double slit with a separation of 0.1 mm
- Incident light has a wavelength of 500 nm
- Calculate the angle of the first-order bright region
- Solution: mλ = d sinθ
- Substitute the given values: 1 × 500 × 10^-9 m = 0.1 × 10^-3 m × sinθ
- Solve for θ: sinθ ≈ (1 × 500 × 10^-9)/(0.1 × 10^-3)
- Calculate θ: θ ≈ 2.86°

Diffraction gratings are devices that consist of many closely spaced slits or lines
When light passes through a diffraction grating, it produces a highly regular and intense diffraction pattern
Diffraction gratings are commonly used in spectrometers to separate light into its component colors
The intensity and width of the bright regions in the diffraction pattern depend on the number of slits or lines in the grating
Diffraction gratings are essential tools in various scientific and technological applications

The study of diffraction provides valuable insights into the behavior of waves
Diffraction phenomena are observed in various contexts, including light passing through small openings, sound waves bending around corners, and water waves encountering obstacles
Understanding diffraction is crucial in fields such as optics, acoustics, and wave mechanics
Scientists and engineers utilize diffraction principles to design and develop numerous devices and systems
Further exploration of diffraction continues to expand our knowledge of the fundamental nature of waves

Sure! Here are slides 21 to 30 on the topic “Diffraction - Geometric shadow of obstacle”: ``

Diffraction patterns can also be observed using circular apertures or obstacles
Circular diffraction patterns exhibit concentric bright and dark rings
The central bright region is larger and more intense compared to the outer rings
The angular spacing between the rings depends on the diameter of the aperture and the wavelength of the incident light
The diffraction pattern of a circular aperture can be described by the Bessel function

Example:
- Consider a circular aperture with a diameter of 5 mm
- Incident light has a wavelength of 700 nm
- Calculate the angular spacing between the first and second bright rings
- Solution: Use the Bessel function to calculate the angular spacing based on the aperture diameter and wavelength of light

Diffraction can also occur at the edges of objects, known as edge diffraction or Fresnel diffraction
Edge diffraction patterns exhibit curved wavefronts and regions of constructive and destructive interference
The diffraction pattern depends on the distance from the edge, the size of the obstacle, and the wavelength of the incident wave
Edge diffraction is commonly observed in various optical phenomena, such as the spreading of light around objects or through small openings

Diffraction effects are utilized in various applications, including:
- Optical gratings used in spectrometers and wavelength analysis
- Diffraction-based optical components, such as lenses and beam splitters
- Diffractive optical elements used in laser systems and imaging devices
- Diffraction-based holography for creating 3D images
- Diffraction patterns in X-ray crystallography for determining atomic structures

Diffraction plays a vital role in understanding the nature of waves and the behavior of light
It provides insights into phenomena like interference, polarization, and scattering
Diffraction is a fundamental topic in the study of optics and wave mechanics
The principles of diffraction are used extensively in various scientific disciplines and technological applications
Ongoing research continues to deepen our understanding of diffraction and its applications

Recap:
- Diffraction is the phenomenon observed when waves encounter obstacles or openings
- Huygens’ principle explains the behavior of waves during diffraction
- Diffraction patterns exhibit both constructive and destructive interference
- Single slit diffraction produces a central bright region with alternating dark and bright regions
- Double slit diffraction results in a pattern of bright and dark regions, with a central maximum and higher-order maxima

Recap:
- Diffraction gratings produce highly regular and intense diffraction patterns
- Diffraction can also occur with circular apertures, resulting in concentric rings
- Edge diffraction or Fresnel diffraction occurs at the edges of obstacles or openings
- Diffraction has various applications in optics and other scientific fields
- Understanding diffraction is crucial for a comprehensive understanding of wave behavior and the properties of light

Let’s solve another example:
- A double slit is illuminated with monochromatic light of wavelength 600 nm
- The distance between the two slits is 0.1 mm
- The distance between the screen and the slits is 2 m
- Calculate the angular width of the second-order bright region
- Solution: Use the equation mλ = d sinθ to calculate the angle, where m = 2 for second-order

Final thoughts:
- Diffraction is a fascinating phenomenon that occurs when waves encounter obstacles or openings
- It is a property of all waves, including light, sound, and water waves
- Understanding diffraction is crucial for various applications in optics, acoustics, and wave mechanics
- Through diffraction, we gain insights into the nature of waves and the fundamental principles of wave behavior
- Ongoing research in diffraction continues to contribute to advancements in science and technology

Thank you for your attention!
Questions?
Let’s continue exploring the fascinating world of physics! ``