Key Idea: This topic is four things waves DO at a boundary, a gap or an edge: they refract (bend when they change speed), interfere (add up where two waves meet), spread through a double slit into evenly spaced fringes, and diffract (fan out through a gap). It is examined on both papers. Paper 1A tends to be quick multiple-choice — which way a ray bends, constructive vs destructive from a path difference, what happens to the fringe spacing, which wave diffracts more. Paper 2 is longer structured work — a Snell's-law or critical-angle calculation, a 'show that' on path difference, plugging into s = λD/d, or an explain on coherence, diffraction or energy conservation across the fringes.
📋 Key formulas
Most of these carry the data-booklet badge (look for it). The critical-angle relation and the small-angle fringe angle are not printed separately — they come straight from the given equations, so you remember those.
- refractive index of medium 1 (no units)
- refractive index of medium 2 (no units)
- angle of incidence, measured from the normal (°)
- angle of refraction, measured from the normal (°)
- refractive index of the medium (no units)
- speed of light in a vacuum, 3.0 × 10⁸ m s⁻¹
- speed of light in the medium (m s⁻¹)
- critical angle (°) — the incidence angle giving a 90° refraction
- index of the denser medium the light starts in
- index of the less-dense medium it tries to enter
- extra distance one wave travels to reach the point (m)
- a whole number: 0, 1, 2, 3, …
- wavelength of the waves (m)
- fringe spacing — gap between neighbouring bright fringes (m)
- wavelength of the light (m)
- distance from the slits to the screen (m)
- separation of the two slits (m)
- angular separation of neighbouring fringes (rad)
- wavelength of the light (m)
- separation of the two slits (m)
- wave speed — how fast the wave travels (m s⁻¹)
- frequency — waves per second (Hz)
- wavelength — length of one full wave (m)
⚖️ The four phenomena side by side
| Phenomenon | What happens | Key relationship | What to remember |
|---|---|---|---|
| Refraction | A wave bends as it changes speed crossing a boundary | n₁ sinθ₁ = n₂ sinθ₂; n = c/v | Measure angles from the normal. Into a denser (higher-n, slower) medium → bends toward the normal. |
| Total internal reflection | Light trapped inside the denser medium, all reflected back | sinθc = n₂/n₁ | Only denser → less-dense AND incidence angle above the critical angle θc. High index → small θc (diamonds sparkle). |
| Interference | Two coherent waves add where they meet | constructive nλ; destructive (n+½)λ | Divide path difference by λ: whole number → constructive (add amplitudes); + ½ → destructive (equal amplitudes cancel). |
| Double slit | Two close coherent slits make evenly spaced fringes | s = λD/d; θ ≈ λ/d | Every length in metres. Smaller slit separation d → wider fringes. Central fringe is brightest. |
| Diffraction | A wave spreads through a gap or round an edge | (no SL formula); v = fλ | Spreading greatest when gap ≈ λ. Longer wavelength (lower frequency) → more spreading through the same gap. |
🌈 Constructive vs destructive — read it off the path difference
| Path difference | As a multiple of λ | Phase | Result |
|---|---|---|---|
| 0, λ, 2λ, 3λ, … | nλ (whole number) | In step (in phase) | Constructive — amplitudes add → bright / loud |
| ½λ, 1½λ, 2½λ, … | (n + ½)λ | Half a cycle out of step (antiphase) | Destructive — equal amplitudes cancel → dark / quiet |
Complete cancellation to zero only happens when the two amplitudes are equal. If they differ, in phase gives the sum and antiphase gives the difference. At a dark fringe the energy is not destroyed — it is redistributed into the brighter bright fringes, so the total energy over the whole screen is conserved.
✏️ Worked exam-style questions
Light inside a glass block of refractive index 1.52 meets the boundary with air (index 1.00). (a) Find the critical angle for this glass–air boundary. (b) A ray inside the glass hits the boundary at 50° to the normal — does it escape into the air or is it totally internally reflected?
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A beam of light travels from air (index 1.00) into a transparent liquid, with an angle of incidence of 58° and an angle of refraction of 36°, both measured from the normal. (a) Find the refractive index of the liquid. (b) Hence find the speed of light in the liquid (c = 3.0 × 10⁸ m s⁻¹).
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Two coherent loudspeakers play the same note of wavelength 0.40 m. At a point P the sound from one speaker has travelled 1.0 m further than from the other. Each speaker alone would give P a wave of amplitude 6.0 units. (a) State whether P is loud or quiet. (b) Find the resultant amplitude at P.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Two slits 0.30 mm apart are lit by a laser. On a screen 1.8 m away the bright fringes are 3.6 mm apart. (a) Find the wavelength of the light. (b) Find, in radians, the angular separation of two neighbouring bright fringes.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
🧠 Quick self-check
Tap each card to reveal the answer.
Light enters a denser (higher-n) medium — which way does the ray bend? Toward the normal — the angle gets smaller, because the light slows down. Measure all angles from the normal, not the surface.
What two conditions are needed for total internal reflection? Light going denser → less-dense, AND an incidence angle above the critical angle θc (sinθc = n₂/n₁, less-dense index on top).
Path difference is 1.5λ between two EQUAL waves — what is the resultant amplitude? Zero. 1.5λ = (1 + ½)λ is destructive, and equal amplitudes cancel completely.
What does 'coherent' mean, and why is it needed? The sources keep a constant phase difference (same wavelength, fixed step). Without it the bright and dark points drift and average out, so no steady pattern is seen.
Move the two slits closer together — what happens to the fringe spacing? It gets wider. In s = λD/d the slit separation d is on the bottom, so a smaller d gives a bigger s.
Same gap: does a higher or lower frequency diffract more? A lower frequency — it has a longer wavelength (λ = v/f), so the gap-to-wavelength ratio falls toward 1 and the wave spreads more. Diffraction is greatest when gap ≈ λ.
🎯 Exam tips
Exam Tips
- Always measure refraction angles from the NORMAL (the dashed line), never from the surface. Into a higher-index (denser, slower) medium the ray bends TOWARD the normal.
- Total internal reflection needs BOTH conditions: denser → less-dense, and an incidence angle above the critical angle. Use sinθc = n₂/n₁ with the LESS-dense index on top — a sine above 1 means you flipped the ratio.
- For interference, divide the path difference by λ: a whole number is constructive (add amplitudes); a whole number + ½ is destructive. Complete cancellation to zero only happens when the two amplitudes are equal.
- Coherent = constant phase difference. State exactly this whenever asked why two sources must be coherent.
- For s = λD/d, convert EVERY length to metres first (mm = 10⁻³ m, nm = 10⁻⁹ m). Smaller slit separation d → wider fringes; the fringe ANGLE λ/d is independent of the screen distance D.
- Energy is not lost at a dark fringe — it is redistributed into the bright fringes, so the total over the screen is conserved.
- Diffraction is greatest when the gap is about the size of the wavelength (gap ≈ λ). Lower frequency → longer wavelength → MORE spreading. (The classic trap is thinking a higher frequency spreads more.)