Applied Physics was the subject that taught us why things work: why fibres carry the internet, why silicon makes a good chip, why a laser is different from a torch. Most of us memorised formulas for the exam and moved on. Here are the ideas worth keeping, each tied to something you use every day.
Light behaves like a wave
Interference. When two light waves meet, they add up. Where crest meets crest they reinforce (constructive interference, a bright band); where crest meets trough they cancel (destructive interference, a dark band). Young’s double-slit experiment shows this as a pattern of bright and dark fringes, with fringe width β = λD/d, where λ is the wavelength, D the distance to the screen and d the gap between the slits.
Real world: the colours on a soap bubble or an oil film on a wet road are thin-film interference. Light reflecting from the top and bottom of the film interferes, and the colour depends on the film’s thickness. The anti-reflection coating on spectacles and camera lenses uses the same effect deliberately, to cancel reflections.
Diffraction. Light bends around edges and spreads after passing through a narrow opening. A diffraction grating, many closely spaced lines, splits white light into its colours.
Real world: the rainbow you see on the back of a CD or DVD is diffraction from its closely packed data tracks. Diffraction also sets the limit on how small a feature a lens can resolve, which is why chipmakers moved to extreme ultraviolet light, with a much shorter wavelength, to print transistors only a few nanometres across.
Polarisation. Light waves vibrate in all directions at right angles to their travel. A polariser lets through only one direction. Two laws to remember:
- Malus’s law: light through a second polariser at angle θ has intensity I = I₀ cos²θ.
- Brewster’s law: reflected light is fully polarised when tan θ = n, the refractive index.
Real world: polarised sunglasses block the horizontally polarised glare reflected from roads and water. Every LCD screen, from a calculator to a laptop, works by twisting polarised light with liquid crystals and passing it through a polariser.
Lasers: light in step
A laser (Light Amplification by Stimulated Emission of Radiation) produces light that is unusually pure and orderly.
- Stimulated emission: an excited atom, hit by a photon of the right energy, releases a second, identical photon in the same direction and phase. Einstein predicted this in 1917.
- Population inversion: normally most atoms are in the lower energy state. A laser needs more atoms in the excited state than below it, so that stimulated emission outweighs absorption. This is achieved by pumping energy in (light, electricity), usually into a long-lived metastable state.
- Optical cavity: two mirrors at the ends bounce the light back and forth, amplifying it, and one partly transparent mirror lets the beam out.
Laser light is monochromatic (one wavelength), coherent (all waves in step), directional (barely spreads) and intense. The first laser, a ruby laser, was built by Theodore Maiman in 1960; the helium-neon laser followed soon after, and semiconductor laser diodes are now the most common type.
Real world: barcode scanners at supermarkets, the laser diodes that send data down optical fibres, LASIK eye surgery, laser printers, and the LiDAR sensors in self-driving cars and recent phones all use lasers.
Fibre optics: the internet’s backbone
An optical fibre is a thin glass core surrounded by cladding with a slightly lower refractive index. Light entering the core strikes the boundary at a shallow angle and undergoes total internal reflection: it bounces along the core, trapped, for kilometres.
- Numerical aperture: NA = √(n₁² − n₂²), where n₁ and n₂ are the core and cladding indices. It measures how wide a cone of light the fibre accepts (the acceptance angle).
- Step-index fibres have a sharp change in index between core and cladding. Graded-index fibres change the index gradually, which reduces the spreading of pulses.
- Single-mode fibres have a very thin core that carries one light path. They are used over long distances. Multimode fibres are thicker, cheaper and used over short runs.
- Attenuation is the loss of signal per kilometre. Modern single-mode fibre loses only about 0.2 dB per kilometre at 1550 nm, so signals travel tens of kilometres between amplifiers.
Real world: almost all internet traffic between cities and continents travels as laser light through fibre, including the undersea cables that land in Mumbai and Chennai. Fibre-to-the-home broadband and the links between servers inside cloud data centres use the same physics.
Crystals: how atoms arrange themselves
Solids such as metals and silicon are crystals: atoms arranged in a repeating 3D pattern.
- The smallest repeating block is the unit cell. There are 7 crystal systems and 14 Bravais lattices.
- The three cubic structures to remember:
| Structure | Atoms per unit cell | Coordination number | Packing fraction | Example |
|---|---|---|---|---|
| Simple cubic | 1 | 6 | 52% | Polonium |
| Body-centred cubic | 2 | 8 | 68% | Iron, sodium |
| Face-centred cubic | 4 | 12 | 74% | Copper, aluminium, gold |
- Miller indices (h k l) name planes in a crystal.
- Bragg’s law, 2d sin θ = nλ, describes how X-rays reflect off crystal planes spaced d apart. Measuring the angles gives the crystal’s structure.
Real world: silicon wafers for chips are grown as single, nearly perfect crystals, because defects ruin transistors. X-ray diffraction revealed the double-helix structure of DNA in 1953, and it is still how drug researchers find the shapes of proteins.
Quantum mechanics: the rules of the very small
Classical physics fails at the scale of atoms and electrons. Quantum mechanics replaces it.
- Wave-particle duality. Particles also behave like waves. A particle with momentum p has a de Broglie wavelength λ = h/p, where h is Planck’s constant.
- Heisenberg’s uncertainty principle. Position and momentum cannot both be known exactly: Δx · Δp ≥ ħ/2.
- Schrödinger’s equation describes how a particle’s wave function behaves. The square of the wave function gives the probability of finding the particle at a point.
- Particle in a box. An electron confined in a box of width L can only have certain energies: Eₙ = n²h² / 8mL². Energy is quantised. The smaller the box, the bigger the gaps between levels.
- Tunnelling. A particle can cross a barrier that, classically, it does not have enough energy to climb.
Real world: electron microscopes use the short de Broglie wavelength of electrons to see far smaller details than light microscopes can. Flash memory, in every SSD and phone, stores data by pushing electrons through a thin insulating layer by quantum tunnelling. Quantum dots in QLED televisions glow in different colours depending on their size, because of the particle-in-a-box effect.
Electrons in solids: why metals conduct and glass does not
Free electron theory. The classical theory (Drude and Lorentz) treated the electrons in a metal as a gas of free particles. It explains Ohm’s law and electrical conductivity, but it gives wrong answers for some properties, such as how much heat electrons can absorb. The quantum free electron theory (Sommerfeld) fixed this by applying quantum rules: electrons fill energy levels from the bottom up, according to the Fermi-Dirac distribution, and the highest filled level at absolute zero is the Fermi level.
Band theory. In a crystal, the energy levels of billions of atoms merge into bands. What matters is the gap between the highest filled band (the valence band) and the next empty one (the conduction band):
| Material | Band gap | Behaviour |
|---|---|---|
| Conductor | Bands overlap, no gap | Electrons move freely |
| Semiconductor | Small gap, about 1 eV (silicon: 1.12 eV) | Conducts when given a little energy (heat, light) |
| Insulator | Large gap, several eV (diamond: about 5.5 eV) | Almost no conduction |
Real world: band theory is why copper is used for wires, glass and plastic for insulation, and silicon for chips. The Kronig-Penney model from your syllabus was the first simple model to show how these bands form.
Semiconductors: the foundation of electronics
- Intrinsic semiconductors are pure, such as pure silicon. They conduct very little.
- Doping adds tiny amounts of other elements:
- n-type: a group V element (phosphorus, arsenic) adds extra electrons.
- p-type: a group III element (boron) creates holes, places missing an electron, which act as positive charges.
- A p-n junction, where p-type meets n-type, lets current flow easily in one direction only. It is the basis of diodes, LEDs, solar cells and transistors.
- The Hall effect: a current-carrying conductor in a magnetic field develops a voltage across it. Its sign shows whether the carriers are electrons or holes, and its size gives their concentration.
Real world: every processor is billions of transistors made from doped silicon. The colour of an LED depends on the band gap of its semiconductor: a bigger gap gives bluer light, which is why the blue LED, which enabled white LED lighting, won the Nobel Prize in 2014. Hall sensors detect when a flip phone or laptop lid closes, measure wheel speed for a car’s ABS, and sense position in brushless motors.
Superconductors: zero resistance
Some materials lose all electrical resistance when cooled below a critical temperature, Tc.
- Heike Kamerlingh Onnes discovered superconductivity in 1911, in mercury at about 4.2 K (−269 °C).
- Meissner effect: a superconductor expels magnetic fields from inside itself. This is why a magnet can float above it.
- Type I superconductors lose superconductivity abruptly in a strong magnetic field. Type II superconductors tolerate much stronger fields, which makes them useful for magnets.
- BCS theory explains it: electrons pair up as Cooper pairs and move through the lattice without scattering.
- High-temperature superconductors, such as YBCO (about 92 K), work above the boiling point of liquid nitrogen (77 K), which is cheap and easy to handle.
Real world: the powerful magnets in MRI scanners are superconducting coils cooled by liquid helium. Japan’s SCMaglev trains float on superconducting magnets. Many of today’s quantum computers use superconducting circuits as qubits, cooled to near absolute zero.
Dielectric and magnetic materials
Dielectrics are insulators that become polarised in an electric field: their charges shift slightly. There are three main mechanisms: electronic, ionic and orientational polarisation. The dielectric constant measures how strongly a material polarises, and therefore how much charge a capacitor can store.
Real world: capacitors in every circuit board use dielectrics. Modern transistors replaced silicon dioxide with high-k dielectrics such as hafnium oxide, so that the insulating layer could stay thick enough to block leakage while transistors kept shrinking.
Magnetic materials are classified by how they respond to a magnetic field:
- Diamagnetic materials are weakly repelled (copper, water).
- Paramagnetic materials are weakly attracted (aluminium).
- Ferromagnetic materials are strongly attracted and can stay magnetised (iron, nickel, cobalt). Their atoms align in regions called domains.
A plot of magnetisation against the applied field, the hysteresis loop, separates two kinds of ferromagnetic material:
- Soft materials have narrow loops. They are easy to magnetise and demagnetise, so they are used for transformer and motor cores.
- Hard materials have wide loops and stay magnetised. They are used for permanent magnets and data storage.
Real world: hard disk drives store every bit as a tiny magnetised region on a platter. The strong neodymium magnets in phone speakers, earbuds and electric-vehicle motors are hard magnetic materials.
Nanomaterials: when size changes the rules
At the nanoscale (1 to 100 nanometres), materials behave differently. They have a huge surface area relative to their volume, and quantum effects (as in the particle in a box) change their colour, strength and conductivity.
- Carbon nanotubes and graphene, a single layer of carbon atoms, are extremely strong and conduct electricity very well.
- Quantum dots change colour with their size.
- Nanoparticles of zinc oxide and titanium dioxide block UV light while staying invisible on the skin.
Real world: the transistors in a current phone processor have features only a few nanometres across, a few dozen atoms wide. Mineral sunscreens use nanoparticles, and QLED televisions use quantum dots.
One-minute recap
| Topic | Key idea | You use it in |
|---|---|---|
| Interference | Waves add or cancel | Anti-reflection coatings, soap-bubble colours |
| Diffraction | Light bends and spreads | CD rainbows, chip lithography limits |
| Polarisation | Light vibrates in one direction | LCD screens, polarised sunglasses |
| Lasers | Stimulated emission, population inversion | Barcode scanners, fibre links, LiDAR |
| Fibre optics | Total internal reflection | Internet backbone, undersea cables |
| Crystals | Unit cells, Bragg’s law | Silicon wafers, X-ray crystallography |
| Quantum mechanics | Duality, quantised energy, tunnelling | Flash memory, electron microscopes, QLED |
| Band theory | Band gap decides conductor, semiconductor or insulator | Choosing copper, silicon or glass |
| Semiconductors | Doping, p-n junction, Hall effect | Chips, LEDs, solar panels, lid sensors |
| Superconductors | Zero resistance, Meissner effect | MRI, maglev, quantum computers |
| Dielectric and magnetic materials | Polarisation, hysteresis | Capacitors, transformers, hard disks |
| Nanomaterials | Size changes properties | Modern transistors, sunscreen |
Next in Engineering Revisited: C Programming & Data Structures.
Written by Claude, Anthropic’s AI assistant, as part of Engineering Revisited, a quick refresher of the B.Tech subjects one at a time.