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


Wave optics, also known as physical optics, is a subfield of optics that studies the wave nature of light. Unlike geometrical optics, which treats light as rays traveling in straight lines, wave optics treats light as a wave that can exhibit interference, diffraction, and polarization.

Introduction to the wave nature of light

Light behaves as both a wave and a particle. This dual nature is one of the fundamental concepts in physics. Wave optics deals primarily with the wave aspect of light.

Huygens' principle

Huygens' principle is a fundamental concept that helps explain how waves propagate. According to this principle, each point on the wavefront can be considered the source of secondary wavelets that propagate in all directions at the speed of light. The new wavefront is formed by the surface tangents of these secondary wavelets.

Huygens' Principle:
1. Consider a point on the wavefront.
2. Consider it as a source emitting a spherical wavelet.
3. The new wavefront is the envelope of these wavelets.

Interference of light

Interference occurs when two or more waves overlap and combine to form a new wave pattern. In wave optics, the principle of superposition is used to describe interference, where the resulting wave is the sum of the individual waves.

The formula for path difference in interference is:

Path Difference (Δ) = d * sin(θ)

where d is the distance between the sources, and θ is the angle of incidence.

Types of intervention

  • Constructive interference: This occurs when wave amplitudes add up, resulting in a wave with a higher amplitude. 
    Condition: Δ = nλ, where n is an integer.
  • Destructive interference: This occurs when wave amplitudes cancel each other out, resulting in a wave with a lower amplitude. 
    Condition: Δ = (n + 1/2)λ

Diffraction

Diffraction is the bending of light waves around the edges of obstacles or through slits. It is a consequence of the wave nature of light and becomes important when the size of the obstacle or slit is comparable to the wavelength of the light.

Single slit diffraction

When light passes through a narrow slit, it spreads out and forms a diffraction pattern on the screen. The central maximum is the brightest part of the pattern. As we move away from the centre, the intensity of light decreases.

Single slit diffraction formula:
sineθ = m(λ/W)
M = ±1, ±2, ±3, ...

where W is the slit width, θ is the angle relative to the incident direction, and m is the order of the minimum.

Double slit diffraction

In a double-slit experiment, light passes through two closely spaced slits, producing an interference pattern due to the overlapping of the diffracted waves.

Condition for maximum: d * sinθ = nλ
Condition for minima: d * sinθ = (n + 1/2)λ

where d is the distance between the slits, θ is the diffraction angle, and n is an integer.

Polarization of light

Polarization refers to the orientation of the oscillations in the wave. In unpolarized light, the electric fields oscillate in many directions. However, polarized light oscillates in a single direction.

Polarization methods

  • Polarization by absorption: Uses polarizing filters to allow waves of a specific orientation to pass through.
  • Polarization by reflection: This occurs when light reflects off a surface at a certain angle, known as the Brewster angle.
  • Polarization by scattering: Scattering of light in the atmosphere may cause it to become partially polarized.

Formula of Brewster angle:

tanθ_b = n2 / n1

where θ_b is the Brewster angle, n2 is the refractive index of the second medium, and n1 is the refractive index of the first medium.

Applications of wave optics

Wave optics is not only a theoretical part of optics, but it has many applications in various fields:

  • Design of optical instruments: Wave optics principles are used in the design of telescopes, microscopes and cameras.
  • Holography: Uses interference patterns to create three-dimensional images.
  • Fiber Optic Communication: Wave optics explains the transmission of light through optical fibers.
  • Diffraction grating: used in spectrometers to analyze the light spectrum.

Mathematical description of waves

Understanding the mathematics behind waves helps to gain deeper insight into wave optics. Light waves can be described using the wave equation:

Wave equation: ∂²E/∂x² = (1/c²)*∂²E/∂t²

where E is the electric field, c is the speed of light, x is position, and t is time.

Superposition Principle

The superposition principle states that the resultant wave at any point is the sum of all the individual waves. This principle is essential to understanding interference.

Coherence of waves

For a continuous interference pattern, the sources of light must be coherent, meaning that they maintain a constant phase difference. Coherent waves can be produced using lasers or other stable light sources.

Coherence length is the length during which the wave maintains a specified degree of coherence, and coherence time is the time during which the wave maintains coherence.

Visualization example

Understanding wave optics can be greatly improved through a visual aid. Below is a simple way to visualize some of the concepts.

Consider the wavefront represented by a simple sine wave:

This wavefront may represent a single wave. If we consider several such wavefronts, you will have an interference pattern, perhaps a series of light and dark bands:

When light undergoes diffraction, it bends around corners or small holes. Here is a simple representation of such wave propagation:

Conclusion

Wave optics allows us to understand the detailed and complex wave nature of light. From the interference patterns that reveal themselves in double slit experiments to the beautiful rainbows that form due to diffraction, wave optics explains many natural and technological phenomena that are integral to both the scientific and everyday worlds.

With its underlying principles, wave optics remains an essential field in both fundamental physics and applied technologies, influencing everything from optical data storage to modern communications systems.


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