Diffraction – An Introduction
Diffraction is the bending or spreading of light waves when they encounter an obstacle or pass through a narrow opening. This phenomenon is a fundamental characteristic of all wave-like behavior and is most noticeable when the size of the aperture or obstacle is comparable to the wavelength of the wave.
🔹 Cause of Diffraction
According to Huygens’ Principle, every point on a wavefront acts as a source of secondary wavelets. When a wavefront is partially blocked or passed through an aperture, these secondary wavelets interfere with each other and create a diffraction pattern.
🔹 Types of Diffraction
1. Fresnel Diffraction (Near-Field Diffraction)
- Source or screen or both are at a finite distance.
- No lens is used.
- Wavefronts are spherical or cylindrical.
- Examples: Diffraction at a slit, wire, or edge; zone plate analysis.
2. Fraunhofer Diffraction (Far-Field Diffraction)
- Source and screen are effectively at infinite distances (lens may be used).
- Involves parallel rays and plane wavefronts.
- Easy to analyze mathematically.
- Examples: Single slit, double slit, diffraction grating.
🔹 Conditions for Diffraction to Occur
- The size of the aperture/obstacle must be similar to the wavelength.
- The incident light should be coherent and monochromatic.
- Proper screen placement is necessary depending on the diffraction type.
🔹 Difference Between Diffraction and Interference
| Property | Diffraction | Interference |
|---|---|---|
| Origin | Bending of waves around obstacles | Superposition of two or more wavefronts |
| Number of Sources | Single source with aperture/obstacle | At least two coherent sources |
| Pattern Symmetry | Often asymmetric | Typically symmetric |
| Intensity Distribution | Gradual variation, central maximum not always brightest | Sharp and distinct maxima and minima |
🔹 Applications of Diffraction
- Used in spectrometers via diffraction gratings.
- Helps determine the resolving power of optical instruments.
- Used in X-ray crystallography.
- Key in designing optical elements like zone plates.
🔹 Conclusion
Diffraction is a fundamental concept in physical optics, essential for understanding the behavior of light beyond the basic laws of reflection and refraction. It explains many natural and scientific phenomena and forms the basis for modern optical engineering.
Fresnel's Diffraction
Fresnel diffraction occurs when either the source of light or the screen (or both) are at a finite distance from the diffracting object. This diffraction is observed in the near-field region, and it does not require any lenses. The wavefronts involved are curved — either spherical or cylindrical.
🔹 Characteristics of Fresnel Diffraction
- Near-field or intermediate region diffraction.
- Wavefronts are curved (not plane).
- No need for lenses.
- Diffraction patterns vary with distance.
- Analyzed using Fresnel zones.
🔹 Fresnel Zone Method
A wavefront is divided into concentric rings called Fresnel zones, each contributing a phase difference of λ/2. The interaction of waves from these zones determines the brightness or darkness at a point.
- Odd-numbered zones constructively interfere.
- Even-numbered zones tend to cancel out adjacent zones.
- Blocking even or odd zones changes intensity.
🔹 Types of Fresnel Diffraction
1. Diffraction at a Straight Edge
Produces a shadow with fringes near the edge. Caused by interference of wavelets around the edge.
2. Diffraction at a Slit
Light passes through a narrow slit and forms a non-uniform diffraction pattern on the screen.
3. Diffraction at a Circular Aperture or Disc
Creates concentric rings. Poisson’s spot (a bright spot at the center of a shadow) appears behind an opaque circular disc.
4. Diffraction at a Wire
Thin wires obstruct light and cause fringes due to bending around the edges.
🔹 Comparison Table
| Property | Fresnel Diffraction | Fraunhofer Diffraction |
|---|---|---|
| Source & Screen | Finite Distance | Infinite Distance |
| Wavefront | Spherical/Cylindrical | Plane |
| Lens Requirement | Not Required | Required |
| Pattern Behavior | Varies with distance | Fixed pattern |
🔹 Applications
- Used in designing zone plates.
- Explains fringe formation near edges and obstacles.
- Used in optical testing and diffraction-based instruments.
🔹 Approximate Fringe Position
x = √(a × Î» × n)
Where:
x = fringe position, a = distance to screen, λ = wavelength, n = zone number
Conclusion: Fresnel diffraction gives valuable insight into wave behavior near obstacles and is essential for understanding shadow formation and light patterns in real-world setups.
Zone Plate and Convex Lens
A Zone Plate is an optical device that focuses light using the principle of diffraction and interference rather than refraction. It mimics the behavior of a convex lens but achieves focus through concentric rings that diffract light constructively.
🔹 Structure of a Zone Plate
It is made of alternating opaque and transparent concentric zones. These zones are designed so that light from each contributes constructively to a focal point, based on Fresnel diffraction.
Radius of nth Zone:
Rn = √(nλf)
Where:
n = zone number, λ = wavelength, f = focal length
🔹 Comparison with Convex Lens
| Aspect | Zone Plate | Convex Lens |
|---|---|---|
| Principle | Diffraction & Interference | Refraction |
| Number of Foci | Multiple (f, f/3, f/5...) | Single main focus |
| Light Requirement | Monochromatic | Polychromatic or Monochromatic |
| Construction | Thin transparent plate with rings | Curved glass or plastic |
| Image Brightness | Lower | Higher |
🔹 Applications of Zone Plates
- X-ray microscopy
- High-resolution imaging where lenses fail
- Holography and wavefront shaping
- Laser optics and beam control
🔹 Limitations
- Low efficiency compared to a lens
- Multiple foci may cause blur
- Chromatic aberration present
Conclusion: A Zone Plate serves as a diffraction-based counterpart to the convex lens. Though not as efficient, it finds niche applications in high-frequency optics and scientific imaging.
Fresnel Diffraction at Apertures and Obstacles
🔸 1. Diffraction at a Straight Edge
- Fringes appear near the boundary of shadow and light.
- Pattern is asymmetrical.
- Explained using Fresnel half-period zones.
🔸 2. Diffraction at a Narrow Wire
A thin wire blocks part of the wavefront. Light bends around both sides of the wire and creates a diffraction pattern that looks similar to double-slit interference.
- Central bright fringe appears directly behind the wire.
- Fringes are formed due to interference from both edges.
🔸 3. Diffraction at a Circular Aperture
When light passes through a small circular hole, it forms a central bright spot surrounded by concentric dark and bright rings (Airy pattern).
- Airy disk: Bright central region
- Pattern depends on aperture size and wavelength
🔸 4. Diffraction at an Opaque Disc – Poisson’s Spot
If a circular opaque disc is placed in the path of light, a bright spot appears at the center of its shadow. This is known as Poisson’s Spot or Arago’s Spot.
- Caused by constructive interference from waves around the disc.
- Historically important in confirming the wave theory of light.
🔸 Summary Table
| Obstacle | Pattern Type | Key Features |
|---|---|---|
| Straight Edge | Fringes near shadow | Asymmetric light-dark bands |
| Narrow Wire | Bright/dark fringes | Central bright fringe appears |
| Circular Aperture | Airy disk | Concentric bright/dark rings |
| Opaque Disc | Poisson’s Spot | Bright spot at center of shadow |
Conclusion: These examples of Fresnel diffraction show how light bends around edges and interacts with geometry, supporting the wave nature of light. Understanding these effects is essential for optics and instrument design.
Fraunhofer Diffraction at a Single Slit
In Fraunhofer diffraction, both the light source and the observation screen are effectively at infinite distances from the slit. This is practically achieved using lenses. When monochromatic light passes through a narrow slit, it spreads and forms an interference pattern on the screen.
🔹 Experimental Setup
- Collimated (plane) wavefront of monochromatic light.
- A narrow vertical slit of width a.
- A lens focuses the diffracted light onto a screen.
🔹 Pattern Description
- Central bright fringe is the most intense and widest.
- Alternate dark and bright fringes appear on both sides.
- Fringe intensity decreases with distance from the center.
🔹 Key Features
- Central maximum is the widest and brightest.
- Secondary maxima are less intense and narrow.
- Dark fringes (minima) appear at angles satisfying a × sinθ = nλ.
🔹 Applications
- Used to calculate wavelength of light.
- Important in understanding resolution and interference.
- Applied in optical spectrometers and diffraction-limited imaging systems.
Conclusion: Fraunhofer diffraction through a single slit reveals the wave nature of light. It is foundational in optics and essential for understanding how apertures affect light propagation and resolution.
Fraunhofer Diffraction at Circular Aperture and Circular Disc
🔸 1. Circular Aperture – Airy Pattern
When a parallel beam of monochromatic light passes through a small circular aperture, it forms a circular diffraction pattern on a distant screen. The central bright region is known as the Airy Disk, surrounded by concentric rings.
- Pattern is radially symmetric.
- Produced by interference of waves from circular edges.
- Most of the light energy is in the central Airy disk.
Angular Radius of First Dark Ring:
sin(θ) = 1.22 × (λ / D)
Where D = aperture diameter, λ = wavelength of light.
🔸 2. Opaque Circular Disc – Poisson’s Spot
When a small opaque disc is placed in the path of light, a bright spot appears at the center of the shadow. This surprising result is called Poisson’s Spot or Arago’s Spot.
- Caused by constructive interference from edges of the disc.
- Proof of the wave nature of light.
- Visible only under ideal conditions (monochromatic and coherent light).
🔸 Comparison Table
| Type | Central Feature | Pattern Shape | Key Equation |
|---|---|---|---|
| Circular Aperture | Bright Airy Disk | Concentric Rings | sin(θ) = 1.22 λ / D |
| Opaque Disc | Poisson’s Spot | Central Bright Spot | Similar concentric interference |
🔸 Applications
- Determines diffraction limits in optical instruments.
- Used in microscope and telescope design.
- Validates the wave theory of light.
- Helps define the point spread function in imaging systems.
Conclusion: Circular aperture and disc diffraction highlight the symmetry of wave interference. They are crucial in optical system design and help explain resolution limitations in real-world imaging.
Plane Transmission Grating
A plane transmission grating is an optical device used to split light into its component wavelengths using diffraction and interference. It consists of a large number of equally spaced, parallel slits etched on a transparent surface like glass.
🔹 Construction
- Thousands of fine, parallel lines ruled on a transparent plate.
- The spacing between two slits is called the grating element (d).
- If N is the number of lines per mm:
d = 1 / N
🔹 Working Principle
When monochromatic light strikes the grating at normal incidence, each slit acts as a secondary source. Constructive interference leads to bright fringes at certain angles, defined by the grating equation:
d × sin(θ) = nλ
Where:
d = slit spacing, θ = diffraction angle, λ = wavelength, n = order
🔹 Diffraction Orders
- n = 0 gives the central, undeviated (zero-order) maximum.
- n = ±1, ±2, ... give higher-order spectra on both sides.
- Higher orders have greater angular spread but may be dimmer.
🔹 Missing Orders
Missing orders occur when the grating maximum condition coincides with a single-slit minimum, causing certain orders to be suppressed.
🔹 Dispersive Power
The ability of the grating to separate two close wavelengths is given by its dispersive power:
dθ / dλ = n / (d × cosθ)
- Higher dispersive power is achieved with smaller d (more lines per mm) and larger order n.
🔹 Applications
- Used in spectrometers and monochromators.
- Essential in optical and atomic spectroscopy.
- Helps in determining the wavelength of unknown light sources.
Conclusion: Plane transmission gratings are key components in optical instruments. They offer high precision in separating and analyzing light based on wavelength, making them invaluable in scientific research and laboratory applications.
Resolution of Optical Images and Rayleigh’s Criterion
In any optical system, the ability to distinguish two closely spaced objects depends on its resolving power. Diffraction sets a natural limit to this resolution. Rayleigh’s Criterion gives a standard for minimum resolvable separation.
🔹 Rayleigh’s Criterion
"Two point sources are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other."
This applies especially to circular apertures, like lenses or the human eye.
Formula:
θmin = 1.22 × (λ / D)
Where:
θmin = minimum angular separation,
λ = wavelength of light,
D = aperture diameter
🔹 Resolving Power (RP)
Defined as the reciprocal of the minimum resolvable angle:
RP = 1 / θmin
🔹 Resolving Power of Optical Instruments
✅ Telescope:
θmin = 1.22 × (λ / D)
- Better resolution with larger objective diameter
✅ Microscope:
RP = (2n × sinθ) / λ
Where n × sinθ is the numerical aperture (NA)
- High NA and immersion oils improve resolution
✅ Prism:
RP = λ / Δλ
- Depends on dispersion and base width
✅ Grating:
RP = n × N
Where n = order, N = number of slits
- Higher order and more lines improve resolution
🔹 Applications
- Microscopes: cell and microbe studies
- Telescopes: separating distant stars
- Spectrometers: analyzing light composition
- Optical systems: fiber optics, laser tech
Conclusion: Rayleigh’s Criterion sets a practical resolution limit for optical devices. Resolving power is essential in scientific instruments and is affected by diffraction, aperture size, wavelength, and design.
Scattering of Light – Rayleigh and Tyndall Effects
Scattering is the redirection of light as it passes through a medium containing particles. This phenomenon explains natural visuals like the blue sky and red sunsets. Two primary types are Rayleigh scattering and the Tyndall effect.
🔸 1. Rayleigh Scattering
This type of scattering occurs when light interacts with particles much smaller than the wavelength (e.g., air molecules).
- Scattering Intensity ∝ 1 / λ4
- Blue light scatters more than red.
- Explains blue sky and red/orange sunsets.
- Occurs predominantly in gases.
Examples:
- Daytime sky appears blue due to scattered blue light.
- Sunsets appear red as shorter wavelengths are scattered away.
- Scattered light is partially polarized.
🔸 2. Tyndall Effect
This occurs in colloidal suspensions where particles are large enough to scatter light but not large enough to settle.
- Scatters shorter wavelengths more.
- Particles are larger than molecules (typically 1–1000 nm).
Examples:
- Visible beams of headlights in fog.
- Laser beams visible in dusty or smoky air.
- Blue eyes – due to scattering in the iris.
🔹 Rayleigh vs Tyndall Scattering
| Property | Rayleigh Scattering | Tyndall Effect |
|---|---|---|
| Particle Size | Much smaller than wavelength | Comparable to or slightly smaller than wavelength |
| Medium | Gases (e.g., air) | Colloids or suspensions |
| Wavelength Dependence | Strong | Moderate |
| Common Examples | Blue sky, red sunset | Fog beams, blue eyes, colloids |
| Discovered By | Lord Rayleigh | John Tyndall |
🔹 Applications
- Weather forecasting and cloud modeling
- Astronomy – understanding atmospheric scattering
- Biomedical optics – imaging and laser diagnostics
- Identifying colloids in chemistry labs
Conclusion: Scattering of light is central to how we perceive the world. Rayleigh and Tyndall scattering explain a wide range of optical phenomena — from the color of the sky to the behavior of light in biological tissues.
For previous unit of physical optics click below 👇
👉 Unit 1 Nature of light (part 1)
👉 Unit 1 Source of light (part 2)
👉 Unit 2 Interference of Light
👉 Unit 4 Polarization of Light
👉 Unit 5 LASERS
