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).
Bend it
- n₁ sin θ₁ = n₂ sin θ₂ (angles from the normal)
- f fixed; v and λ change
- TIR above θc, into the faster medium
Add it
- Coherent: constant phase difference
- nλ constructive, (n + ½)λ destructive
- Double slit: s = λD/d
Spread it
- Most spreading when the gap ≈ λ
- Wavelength unchanged by diffraction
- Longer λ spreads more
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 (°)
- 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)
- distance from the slits to the screen (m)
- separation of the two slits (m)
- wave speed — how fast the wave travels (m s⁻¹)
- frequency — waves per second (Hz)
HL also gives these:
- slit width (m)
- grating slit spacing (m)
- order: 0, 1, 2, …
Not in the booklet: work them out from the ones above.
- 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
- angular separation of neighbouring fringes (rad)
- wavelength of the light (m)
- separation of the two slits (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.
Next:
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.
Next:
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.
Next:
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.
Important: Every angle in Snell's law is measured from the normal. If a question gives an angle to the surface, use 90° minus it.
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.)