Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Optics → Wave optics ↓


Diffraction


Diffraction is a fundamental concept in wave optics, a branch of optical science that deals with the study of waves, particularly light waves, and their interactions. It is the bending of waves around obstacles and the spreading of waves when passing through small holes. This phenomenon is important in explaining many physical behaviors of waves and has many applications in a variety of fields, including physics, engineering, and even biology.

Basic understanding of waves

Before delving deeper into diffraction, it is important to understand what waves are. A wave can be described as a disturbance that travels through a medium or space, transferring energy from one point to another. In optics, we are primarily concerned with light waves. Light is an electromagnetic wave which means it travels as oscillating electric and magnetic fields.

Waves have specific characteristics such as wavelength (the distance between two successive peaks or troughs), frequency (the number of waves passing a point per second), amplitude (the height of the wave) and speed (the distance traveled by the wave in a given time).

The concept of diffraction

Diffraction occurs when a wave hits an obstacle or hole whose size is comparable to its wavelength. This results in the wave bending and spreading out as it passes the edge of the obstacle or hole. This can be observed with light, sound, and water waves. The diffraction limit increases as the size of the obstacle or hole approaches the wavelength of the wave.

Principle of superposition

To understand diffraction, we must also consider the principle of superposition which states that when two or more waves overlap, the resulting wave is the sum of the individual waves. This principle plays an important role in wave behavior and is particularly important in understanding interference, which is another wave phenomenon closely related to diffraction.

Diffraction pattern

When a wave undergoes diffraction, it often forms a characteristic pattern of interference known as a diffraction pattern. These patterns consist of regions of high intensity (bright fringes) and low intensity (dark fringes). The simplest and most classic example is the single-slit diffraction pattern.

Single-slit diffraction

Let us consider the case of monochromatic light (light of a single wavelength) passing through a narrow slit. As this light passes, it spreads out and forms a pattern on the screen. The central maximum is the brightest and widest part of the pattern, while the subsequent maxima on either side gradually diminish in brightness and width.

Intensity formula for single-slit diffraction is given by: I(θ) = I₀ (sin(β)/β)² where β = (πa/λ) sin(θ) I(θ) = Intensity at angle θ I₀ = Maximum intensity at the center a = Width of the slit λ = Wavelength of the light θ = Angle of diffraction

Double-slit diffraction

In the double-slit experiment, light passes through two closely spaced slits, resulting in an interference pattern of bright and dark fringes on the screen. This phenomenon is explained by two effects: diffraction at each slit and interference between the waves emerging from the two slits.

The resulting pattern shows alternating bright and dark fringes due to constructive and destructive interference. When the waves from the two slits reinforce each other, a bright fringe is produced due to constructive interference. Conversely, when they cancel each other out, a dark fringe appears due to destructive interference.

Fringe spacing formula for double-slit diffraction is given by: Δy = (λL/d) where Δy = Fringe spacing L = Distance from slits to the screen d = Separation between slits

Diffraction grating

A diffraction grating is an optical component with a regular pattern that diffracts light into multiple rays traveling in different directions. The directions of these rays depend on the gap in the grating and the wavelength of the light. Gratings are commonly used in optical instruments such as spectrometers to disperse light into its component wavelengths.

Function of diffraction grating

Diffraction gratings work by splitting and diffracting light into multiple rays traveling in different directions. The angle at which the light is diffracted depends on the wavelength, allowing the grating to be used to separate light into its spectrum.

The diffraction grating formula is given by: d sin(θ) = mλ where d = Distance between grating lines θ = Angle of diffraction m = Order of the spectrum λ = Wavelength of light

Practical examples of diffraction

Diffraction is not just a theoretical concept; it has practical implications in the real world. Here are some examples:

  • Diffraction of sound waves: Sound waves can bend around obstacles such as walls or buildings due to diffraction. This is why you can hear someone speaking, even if they are around the corner.
  • Water waves: Water waves show diffraction. When waves pass through a narrow gap in a pond, they spread out on the other side.
  • X-ray diffraction: Scientists use the X-ray diffraction technique to study the arrangement of atoms in a crystal. The regular atomic structure of a crystal acts like a diffraction grating for X-ray light.
  • Astronomy: To form clear images of distant celestial objects, telescopes must be designed to minimise diffraction effects.

Discovery of the mathematics of diffraction

The theory of diffraction is deeply rooted in mathematical principles. Below is a deeper look at the mathematics behind diffraction:

Fraunhofer diffraction

Fraunhofer diffraction considers the scenario where both the source and the observation point are at infinite distance from the obstacle. It is usually studied for practical situations where lenses can be used to project images of the diffracted light. The equations used to describe this type are simpler than the equations used in Fresnel diffraction.

Fresnel diffraction

Fresnel diffraction deals with the study of diffraction patterns when the wavefronts are not parallel, i.e., the source or the observation point or both are at a finite distance from the obstacle. It requires complex mathematical treatment involving the Fresnel integral.

Visualization of diffraction

To get a clear mental picture of how diffraction works, let's consider an example:

KilnDiffraction

In the figure above, a wave is incident on a slit at the center. The wave spreads out (diffracts) after passing through the slit. The red circle shows the location of the slit where diffraction occurs.

Factors affecting diffraction

Several factors can affect the extent and appearance of the diffraction pattern:

  • Wavelength and aperture size: The ratio of wavelength to the size of the aperture or obstacle significantly affects diffraction. The closer the aperture size is to the wavelength of light, the greater the degree of diffraction.
  • Distance: The distance from the aperture to the point where diffraction is observed affects the pattern. As the distance increases, the pattern spreads further out.
  • Medium: The medium through which the wave travels can also affect diffraction. Different mediums can affect the speed and extent of wave propagation.

Conclusion

Diffraction is an essential phenomenon in the study of wave optics, which describes how waves propagate in different situations. It is the basis of many technologies and scientific techniques. By understanding diffraction, we uncover the behavior and properties of waves, helping us harness their potential in a variety of scientific and practical applications.


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Diffraction

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