Physics 3 (Grade 12)
States of matter, waves, sound, light, mirrors, lenses and interference, then static electricity and electric fields.
States of matter, waves, sound, light, mirrors, lenses and interference, then static electricity and electric fields.
Units of the book
| Unit | What to know |
|---|---|
| States of matter | pressure, Pascal, Archimedes, Bernoulli, solids |
| Vibrations and waves | Hooke’s law, pendulums, wave properties and behaviour |
| Sound | its properties, the Doppler effect, resonance in air columns and strings |
| Light | illuminance, wave nature, polarization |
| Reflection and mirrors | plane and spherical mirrors, the mirror equation |
| Refraction and lenses | Snell’s law, total internal reflection, lenses and eye defects |
| Interference and diffraction | double slit, thin films, gratings |
| Static electricity | charging, Coulomb’s law |
| Electric fields | field strength, potential difference, capacitors |
| Electricity and magnetism | current and Ohm’s law, series and parallel circuits, power, magnetic force, induction and transformers |
| Modern and nuclear physics | quantum theory, the photoelectric effect, the atom, semiconductors, decay and reactors |
Formulas to remember
- P = F/A: pressure
- F₁/A₁ = F₂/A₂: Pascal’s principle
- F b = ρVg: buoyancy (Archimedes)
- F = kx: Hooke’s law
- T = 2π√(L/g): pendulum
- v = fλ: wave speed
- λ = 4L / λ = 2L: closed / open pipe
- 1/f = 1/d₀ + 1/dᵢ: mirror and lens equation
- f = R/2: focal length
- n = c/v: refractive index
- F = kq₁q₂/r²: Coulomb’s law
- E = F/q, ΔV = W/q, q = CV: field, potential, capacitor
🧠 Memory kit: fluids, waves and light
| Formula | In plain words | How to remember it |
|---|---|---|
| P = F / A | Pressure = force per area (pascals). | A needle pierces because its area is tiny. |
| P = ρgh | Fluid pressure at depth h. | A diver feels more pressure the deeper they go. |
| F₁ / A₁ = F₂ / A₂ | Pascal’s principle (hydraulic press). | The big piston gives a big force: the same pressure on more area. |
| F b = ρ fluid V g | Buoyant force (Archimedes) = weight of fluid pushed aside. | An object floats if it is less dense than the fluid. |
| برنولي | The faster a fluid moves, the lower its pressure. | Why a wing lifts: faster air on top means lower pressure there. |
| ΔL = αLΔT | Linear thermal expansion. | That is why bridges and rails have gaps. |
| F = −kx | Hooke’s law: spring force is proportional to stretch, opposite in direction. | k = stiffness: big k → a stiff spring. |
| T = 2π√(L / g) | Period of a simple pendulum; independent of mass and (small) amplitude. | Only the length matters: a longer pendulum swings slower. |
| T = 2π√(m / k) | Period of a mass on a spring. | A heavier mass swings slower, a stiffer spring faster. |
| v = fλ, T = 1/f | Wave speed = frequency × wavelength. | In one medium the speed is fixed: higher frequency → shorter wavelength. |
| v sound ≈ 343 m/s | Speed of sound in air at 20 °C; faster in liquids and faster still in solids; it cannot cross a vacuum. | Sound needs particles to pass it on: closer particles pass it faster. |
| L = λ/4 (مغلق), L = λ/2 (مفتوح) | Resonance in a pipe closed at one end (first resonance), and in an open pipe or string. | Closed → a quarter; open pipe or string → a half. |
| دوبلر | Source approaching → higher pitch; moving away → lower. | An ambulance siren: high as it comes, low as it goes. |
| c = 3 × 10⁸ m/s | Speed of light in a vacuum. | “3 followed by 8 zeros.” |
| E = P / 4πr² | Illuminance: drops with the square of the distance. | Double the distance → a quarter of the light (like gravity). |
| 1/f = 1/d₀ + 1/dᵢ, m = hᵢ/h₀ = −dᵢ/d₀ | Mirror and lens equation, and magnification. | Positive image distance → real image; negative magnification → upside down. |
| f = R / 2 | Focal length of a spherical mirror = half the radius of curvature. | “The focus is halfway to the centre.” |
| n = c / v, n₁ sinθ₁ = n₂ sinθ₂ | Refractive index and Snell’s law. | Entering a denser medium (bigger n), light bends towards the normal. |
| sinθc = n₂ / n₁ | Critical angle; total internal reflection happens only going from denser to less dense. | This is how optical fibres work. |
🧠 Memory kit: electricity, magnetism and modern physics
| Formula | In plain words | How to remember it |
|---|---|---|
| F = kq₁q₂ / r², k = 9 × 10⁹ | Coulomb’s law for the force between charges. | Same shape as gravitation, but like charges repel. |
| e = 1.6 × 10⁻¹⁹ C | The charge on one electron (size). | Number of electrons = total charge ÷ e. |
| E = F / q, ΔV = W / q, C = q / ΔV | Electric field, potential difference, capacitance. | All are “per coulomb”, except capacitance: coulombs per volt. |
| I = q / t | Current = charge passing per second (amperes). | Like the water flowing through a pipe per second. |
| V = IR | Ohm’s law. | Triangle with V on top and I × R below: cover the one you want. |
| P = IV = I²R = V²/R | Electrical power. | Start from P = IV (“piv”) and substitute Ohm’s law. |
| E = Pt (kWh) | Energy used; the kilowatt-hour is the unit on the bill. | A 2 kW device for 3 hours = 6 kWh. |
| R = R₁ + R₂ + … | Series: total = the sum; the same current everywhere; voltages add up. | Series is one road: every resistor is another obstacle. |
| 1/R = 1/R₁ + 1/R₂ + … | Parallel: the same voltage on each branch; currents add; the total is smaller than the smallest. | Parallel is many roads: each extra road makes it easier. For two: R₁R₂ / (R₁ + R₂). |
| F = BIL, F = qvB | Magnetic force on a current-carrying wire and on a moving charge (perpendicular to the field). | The right-hand rule gives the direction; a charge at rest feels nothing. |
| EMF = BLv | Induced EMF in a wire moving through a magnetic field. | Move it or change the field → a current appears (Faraday). |
| V s / V p = N s / N p = I p / I s | Transformer: voltage ratio = turns ratio; current goes the other way. | More secondary turns → step-up voltage, lower current; same power. |
| E = hf = hc / λ, h = 6.63 × 10⁻³⁴ J·s | Energy of a photon. | Higher frequency (violet) → more energy; longer wavelength (red) → less. |
| KE max = hf − W₀ | Photoelectric effect: electron energy = photon energy − work function. | Below the threshold frequency no electrons escape, however bright the light. |
| λ = h / mv | de Broglie wavelength of a particle. | Every moving thing has a wave; big things have tiny ones. |
| E n = −13.6 / n² eV | Energy levels of hydrogen (Bohr). | Dropping a level → a photon is given out; rising → one is absorbed. |
| N = N₀ (½)^(t / T½) | Radioactive decay after a number of half-lives. | Each half-life halves it: 100 → 50 → 25 → 12.5. |
| E = mc² | Mass–energy equivalence (where fission and fusion energy comes from). | A tiny mass × a huge number squared = enormous energy. |
🧠 Memory kit: facts asked again and again
| Topic | What to know |
|---|---|
| Mirrors and lenses | a concave mirror and a convex lens converge light and make real, inverted images (unless the object is inside the focus). A convex mirror and a concave lens diverge and always give virtual, upright, smaller images. |
| Colours of light | primaries: red, green, blue. Red + green = yellow, red + blue = magenta, green + blue = cyan, all three = white. |
| Pigments | primaries: cyan, magenta, yellow; mixing all gives black (subtraction). |
| Waves | transverse: vibration across the direction of travel (light, rope). Longitudinal: along it (sound, slinky). Only transverse waves (light) can be polarized. |
| Radiation | alpha: helium nucleus, +2, stopped by paper. Beta: electron, −1, stopped by aluminium. Gamma: a wave, no charge, needs thick lead. |
| Semiconductors | n-type: doped with group 15 (phosphorus, arsenic), extra electrons. p-type: group 13 (boron, gallium), extra holes. A diode passes current one way; a transistor amplifies or switches. |
| Fission and fusion | fission: a heavy nucleus (uranium) splits (reactors). Fusion: light nuclei (hydrogen) join (the Sun). |
- Series and parallel in one line: “series: the current is shared; parallel: the voltage is shared”. Everything else follows from Ohm’s law.
- Concave = cave: a concave mirror curves in like a cave and gathers light; a convex one bulges out and spreads it.
- Alpha, beta, gamma in order: the charge falls (+2, −1, 0) and the penetration rises (paper, aluminium, lead).
A way of memorizing that sticks
- Understand before you memorize: read “in plain words” for each formula and say out loud what it measures and why each quantity is multiplied or divided. A formula you understand takes a minute to learn.
- Active recall: cover the formula column and write it from memory, then check. Writing from memory beats rereading by far.
- Spaced repetition: review the same sheet after 1 day, 3 days, a week and two weeks. Four short reviews lock it in until test day.
- Your own formula page: write every formula of a book on one page by hand. If it does not fit, you are writing things you can derive, so cut them.
- Teach it: explain the formula to a friend, or to yourself in a mirror, in two sentences. If you cannot explain it, you do not know it yet.
- Use it at once: after each group, press “Try one” in the patterns below. Memory sets when you use it.
Question patterns
Fluids
A hydraulic lift multiplies force by the ratio of the areas.
Springs and waves
Pendulum period ∝ √length: length × 4 ⇒ period × 2.
Sound
An echo travels the distance twice. Beats = difference of frequencies.
Refraction, mirrors and lenses
One equation for mirrors and lenses. Short sight → concave lens; long sight → convex lens.
Illuminance and interference
Illuminance ∝ 1/r². Soap-bubble colours come from thin-film interference.
Static electricity and fields
Distance × 2 ⇒ force ÷ 4. ΔV = W/q, q = CV.
- Angles of incidence and reflection are measured from the normal, not the surface.
- Sound cannot travel through a vacuum; light can.
Electricity and magnetism formulas
- V = IR: Ohm’s law
- R = R₁ + R₂ + …: series
- 1/R = 1/R₁ + 1/R₂: parallel
- P = VI = I²R: power
- E = Pt: energy
- F = BIL: force on a wire
- v = E/B: velocity selector
- Vs/Vp = Ns/Np: transformer
Modern and nuclear physics
- E = hf: photon energy
- W = hf₀: work function
- KE = hf − hf₀: photoelectric effect
- λ = h/p: de Broglie
- α: A − 4, Z − 2: alpha
- β: Z + 1: beta
- γ: no change: gamma
- β = I C /I B: transistor gain
More patterns (figures and calculations)
Ohm’s law
V = IR
Series and parallel
Series: add. Parallel: smaller than the smallest.
Power and the electricity bill
I = P/V, kWh = SAR ÷ price
Magnetism and transformers
F = BIL, Vs/Vp = Ns/Np
Quanta and photons
W = hf₀, λ = h/p, ΔE = E f − E i
Radioactive decay
Alpha −4 and −2; beta raises Z by 1; gamma changes nothing.
Mirrors and sound
Object beyond C → image between F and C; at F no image; inside F virtual. Sound speed 331 + 0.6T
Transistors
Use the same units, then divide collector current by base current.