In simple terms
A friendly intro before the formal notes — no formulas yet.
Why Light Bends, Bounces and Spreads
Waves rarely travel in perfectly straight lines. At a boundary they bounce (reflection) or bend (refraction); through a narrow gap they fan out (diffraction); and where two waves overlap they add up (superposition) into a pattern of bright and dark. Four simple rules — the law of reflection, Snell's law, the gap-to-wavelength ratio, and the path-difference condition — capture almost every question in this topic.
Picture straight ranks of ocean swell rolling towards a beach. Where they hit a sea wall at an angle they reflect off symmetrically. Where they cross from deep into shallow water they slow down and swing round to a new direction — that is refraction. Squeeze them through a narrow harbour mouth and they fan out into curved arcs — that is diffraction. And where two sets of arcs cross, the water piles up in some places and cancels in others — that is interference. Light does exactly the same, just on a scale too small to see directly.
- 1
Decide what the wave meets: a mirror-like boundary (reflection), a transparent boundary where it speeds up or slows down (refraction), a narrow gap (diffraction), or another wave (interference).
- 2
For refraction, put the two media into Snell's law , measuring both angles from the normal.
- 3
Going from a slow (dense) medium towards a fast (less dense) one, check whether the angle exceeds the critical angle — if so the ray is totally internally reflected.
- 4
For overlapping waves, find the path difference: a whole number of wavelengths gives a bright fringe (constructive), an odd number of half-wavelengths gives a dark fringe (destructive).
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step 1
Decide what the wave meets: a mirror-like boundary (reflection), a transparent boundary where it speeds up or slows down (refraction), a narrow gap (diffraction), or another wave (interference).
53 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
53 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- PhETStart here · 1IB C.3
Bending Light
Aim a laser at a boundary; read the angles, change the materials and find total internal reflection.
Why this one: Aim the laser into glass, increase the angle and find the critical angle where refraction becomes total internal reflection.
Try this
- Air → water at 30°: read the refracted angle and check n₁ sin θ₁ = n₂ sin θ₂.
- Switch to glass → air and increase the angle until the refracted ray vanishes — the critical angle.
- Turn on the “Speed” tool — light is slower in the denser medium.
Look for Snell’s law; total internal reflection beyond the critical angle when going from dense to less dense.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- The Physics ClassroomStart here · 29702 8.3 · IB C.3
Ripple Tank Simulator
Two point sources vibrate in a ripple tank; view the pattern and find the nodal and antinodal lines
Why this one: Find the nodal lines where the path difference from the two sources is an odd number of half wavelengths.
Try this
- Start the sources and find a nodal line.
- Find an antinodal line.
- Count the nodal lines.
Look for Nodal lines lie where the path difference is an odd number of half wavelengths.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomStart here · 39702 8.3 · IB C.3
Young's Experiment
Make a few simple measurements on a two-slit pattern and calculate the wavelength of light
Why this one: Measure fringe spacing, slit separation and screen distance, then recover the wavelength from s = lambda-D/d.
Try this
- Measure the fringe spacing on the pattern.
- Record the slit separation and the distance to the screen.
- Calculate the wavelength.
Look for Fringe spacing equals λD divided by the slit separation.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- oPhysicsStart here · 49702 8.4 · IB C.3
Diffraction Grating Laser Lab
3D laser + diffraction grating lab: place the grating, measure spot positions, deduce wavelength or slit spacing
Why this one: Place the grating, measure the first and second-order spots and recover λ from d sin θ = nλ.
Try this
- Place the grating and measure the first-order spot position.
- Use d sin θ = nλ to deduce the wavelength.
- Measure the second-order spot and check.
Look for Spot angles satisfy d sin θ = nλ, so higher orders sit at larger angles.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- SimuPhysicsStart here · 59702 8.2 · 9702 8.3 · IB C.3
Ripple Tank Simulation
Place barriers, gaps and different depth regions in a ripple tank and watch waves reflect, refract and diffract
Why this one: Narrow the gap towards one wavelength and watch the waves spread into a semicircle.
Try this
- Place a barrier and watch the reflection.
- Add a gap and watch the diffraction.
- Add a shallow region and watch the refraction.
Look for Diffraction through a gap is greatest when the gap is about one wavelength wide.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
More simulations48 more on this topic — core ones first
- PhETCore9702 22.3 · 8.3 · IB E.2 · C.3
Quantum Wave Interference
Send photons, electrons or neutrons through single or double slits one at a time and watch the interference pattern build.
Try this
- Choose electrons and double slits — fire them one at a time and watch the screen.
- Let a few hundred arrive — fringes appear out of individual dots.
- Turn on the detector at one slit — the fringes vanish.
Look for Single particles arrive as dots but accumulate into a wave pattern: wave–particle duality.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- oPhysicsCore9702 8.3 · 9702 7.1 · IB C.3
Wave Pulse Interference and Superposition
Two wave pulses pass through each other; adjust heights/widths and watch the superposed sum
Try this
- Set both pulse heights positive and watch them cross.
- Make one height negative and cross again.
- Widen one pulse and compare the sum.
Look for The displacement at each point is the sum of the two pulses, and each pulse emerges unchanged after they cross.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Wave Pulse Interference and Superposition 2
Two pulses on one string in opposite directions; the bottom string shows their point-by-point sum
Try this
- Run the pulses towards each other and watch the bottom string.
- Pause when the pulses overlap fully.
- Run again and compare the bottom string before and after.
Look for The bottom string is the point-by-point sum, so equal pulses of opposite sign cancel momentarily at full overlap.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Wave Pulse Superposition Practice
Draw or pick two pulse shapes, predict the superposition and then check it
Try this
- Pick two pulse shapes and sketch their sum, then check it.
- Draw your own pulses with opposite signs and check.
- Try two pulses of different widths.
Look for The superposition at each point is the algebraic sum of the two pulse displacements.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Wave Interference in 3D
Two-source surface-wave interference in 3D; adjust frequency, source separation and amplitude
Try this
- Increase the source separation and count the lines of calm water.
- Raise the frequency with the separation fixed.
- Change the amplitude.
Look for More nodal lines appear as separation grows or wavelength shrinks; amplitude changes the height but not the pattern.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Interference & Superposition 1
Tutorial with applet: superposition of overlapping pulses, constructive and destructive interference
Try this
- Overlap two upright pulses.
- Overlap an upright and an inverted pulse.
- Pause at the moment of full overlap.
Look for Like pulses add constructively and unlike pulses add destructively at the moment of overlap.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Full topic notes
Formal explanation with the rigour you need for the exam.
Reflection and the law of reflection
When a wave meets a boundary, some of it is always reflected. The law of reflection states that the angle of incidence equals the angle of reflection, with both angles measured from the normal — the line drawn perpendicular to the surface at the point where the ray strikes. The incident ray, the reflected ray and the normal all lie in the same plane. Measuring from the normal rather than from the surface is essential: it is the convention used everywhere in this topic, including in Snell's law.
Angle of incidence = angle of reflection, both measured from the normal.
The incident ray, reflected ray and normal are coplanar.
Reflection occurs at every boundary — even one that mostly transmits light still reflects a little.
A rough surface reflects each ray by the same law but in scattered directions (diffuse reflection); a smooth surface gives a clear image (specular reflection).
Refraction, the refractive index and Snell's law
When light crosses from one transparent medium into another it changes speed, and unless it strikes along the normal this change of speed bends the ray. The refractive index of a medium, , measures how much light slows down in it: is the speed of light in a vacuum and its speed in the medium. Because light never travels faster than , ; a larger means slower light and an optically denser medium. Light slowing down (entering a denser medium) bends towards the normal; light speeding up (entering a less dense medium) bends away from the normal.
Refractive index: ; n = \dfrac{c}{v} \[4pt] Snell's law:
In Snell's law, is the angle in the medium of index and is the angle in the medium of index , both measured from the normal. The single rule that prevents most errors: each refractive index must be paired with the angle in that same medium. Keep the subscripts consistent from the first line of working and the algebra takes care of itself.
Total internal reflection and the critical angle
When light travels from a denser medium towards a less dense one, it bends away from the normal, so the refracted angle is larger than the angle of incidence. Increase the angle of incidence and eventually the refracted ray reaches 90°, grazing along the boundary. The angle of incidence that produces this is the critical angle, . Beyond it there is no refracted ray at all: the light is entirely reflected back into the denser medium. This is total internal reflection.
At the critical angle the refracted angle is , so Snell's law gives:
TIR needs two conditions together: light must travel from a denser to a less dense medium (), AND the angle of incidence must EXCEED the critical angle.
At exactly the refracted ray runs along the boundary; only ABOVE is the reflection total.
Because needs , there is no critical angle when going into a denser medium.
TIR is how optical fibres trap light and how prisms replace mirrors in binoculars and periscopes.
Diffraction: spreading through a gap
Diffraction is the spreading of a wave as it passes through a gap or bends around an obstacle. Crucially, the amount of spreading depends on the ratio of the gap width to the wavelength . When the gap is much wider than the wavelength () the wave passes almost straight through with only slight fraying at the edges. As the gap narrows towards the wavelength () the spreading becomes dramatic, with the wave fanning out in wide arcs on the far side. This is why sound (long wavelength) bends round a doorway readily, while light (very short wavelength) needs an extremely fine slit before its diffraction is visible.
Diffraction is greatest when the gap width is about equal to the wavelength ().
A gap much larger than the wavelength produces almost no noticeable spreading.
Longer wavelengths diffract more than shorter ones through the same gap.
Diffraction is what limits how narrowly light can be focused, and it is the first stage in the double- and single-slit patterns.
Superposition and interference
When two or more waves meet, the principle of superposition states that the resultant displacement at any instant is the vector sum of the individual displacements. Where two crests coincide the wave is reinforced (constructive interference); where a crest meets a trough they cancel (destructive interference). For a fixed, observable pattern the sources must be coherent — same frequency and a constant phase difference. Which type of interference occurs at a given point is decided by the path difference: the extra distance one wave travels compared with the other to reach that point.
For two coherent, in-phase sources: with
Young's double-slit experiment
Thomas Young passed monochromatic light through two very narrow, closely spaced slits. Light diffracts at each slit, so the two slits behave as coherent sources whose waves overlap and interfere. On a distant screen this produces a pattern of equally spaced bright and dark fringes: bright where the path difference is a whole number of wavelengths, dark where it is an odd number of half-wavelengths. The experiment is one of the strongest pieces of evidence that light is a wave.
The spacing between adjacent bright fringes is: where is the wavelength, the perpendicular slit-to-screen distance and the slit separation. The relation holds when .
Single-slit diffraction and the diffraction grating (HL)
This section is HL only. Passing monochromatic light through one narrow slit of width produces a diffraction pattern: a broad, bright central maximum flanked by dimmer secondary maxima separated by dark minima. The first minimum sits at an angle (in radians) from the centre, which makes the central maximum twice as wide as the secondary ones. Narrowing the slit or using a longer wavelength widens the whole pattern — the same gap-to-wavelength dependence seen in diffraction generally.
Single-slit first minimum: \[4pt] Diffraction grating maxima:
A diffraction grating replaces two slits with thousands of equally spaced ones. Every slit contributes light that interferes, and the many-slit interference makes the bright maxima far sharper, brighter and more widely separated than a double slit. Their positions obey , where is the spacing between adjacent slits, the angle of the -th order maximum from the straight-through direction, and Gratings are often quoted as lines per metre, in which case ; convert to a spacing in metres before substituting.
For a grating specified as lines per millimetre, first convert to lines per metre, then take the reciprocal to get in metres. And remember the grating equation caps the number of visible orders: since , the highest order is the largest integer for which .
Common mistakes examiners penalise
Pairing the wrong index with the wrong angle in Snell's law — goes with , the angle in medium 1. Swapping them inverts the bending. Write the subscripts first and keep them consistent.
Measuring angles from the surface instead of the normal — every angle in reflection, refraction and TIR is measured from the normal. An angle taken from the surface is out.
Quoting only ONE condition for total internal reflection — TIR needs BOTH: light going from a denser to a less dense medium AND an angle of incidence greater than the critical angle. Stating only 'angle greater than ' loses the mark.
Thinking diffraction is greatest for a wide gap — spreading is greatest when the gap is about equal to the wavelength (); a wide gap barely diffracts at all.
Confusing the interference conditions — constructive interference is path difference (a WHOLE number of wavelengths); destructive is . Do not read 'even ' as destructive.
Forgetting to convert nm and mm to metres in — mixed units are the single biggest source of wrong double-slit answers.
Applying with as lines per metre — is the slit SPACING in metres, i.e. the reciprocal of the number of lines per metre.
Model answer — marked the way our engine marks it
In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means a wrong number early on does not have to cost you the marks that follow. But that protection only exists if your method is written down, and in an 'explain' part the reasoning marks are separate from the calculation marks. Study how each mark below is earned by a specific line.
Where this leads
These wave phenomena reappear throughout physics. Total internal reflection underpins optical fibres and modern communications; interference and path difference return in thin films, standing waves and, at HL, in the resolution of optical instruments. The habit built here — measure angles from the normal, pair each index with its own angle, and let the path difference decide constructive from destructive — carries directly into every later wave and optics problem. Master the method, show every line, and the rest of wave physics becomes variations on rules you already own.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A ray of light in air () strikes the flat surface of a glass block () at an angle of incidence of 40°. Calculate the angle of refraction inside the glass. [3]
- 1
List the quantities and pair each index with its own angle. Medium 1 (air): , . Medium 2 (glass): ,
Two loudspeakers are driven in phase by the same signal generator, emitting sound of wavelength 0.25 m. A listener stands where the distances to the two speakers are 4.60 m and 4.85 m. State and explain whether the listener hears a loud sound or a quiet sound at this point. [4]
- 1
Find the path difference. m. [M1: path difference calculated]
Light of wavelength 633 nm from a laser passes through two slits separated by 0.45 mm. An interference pattern forms on a screen 2.5 m away. Calculate the spacing between adjacent bright fringes. [3]
- 1
List the quantities and convert to SI units. m m m
Light passes from glass () into air (). Calculate the critical angle, and explain what happens to a ray striking the boundary at an angle greater than this. [4]
- 1
Model answer — full working.
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- Law of reflection
The angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal all lie in the same plane. Both angles are measured from the normal, not from the surface.
- Refractive index ()
— the ratio of the speed of light in a vacuum to its speed in the medium. It is always ; a larger means light travels more slowly and the medium is optically denser.
- Snell's law
. Light bends TOWARDS the normal on entering a denser (higher ) medium and AWAY from the normal on entering a less dense medium. All angles are measured from the normal.
- Critical angle ()
The angle of incidence in the denser medium for which the refracted ray travels along the boundary (). From Snell's law, (with ).
- Total internal reflection (TIR)
When light meeting a boundary is entirely reflected back into the original medium. It requires TWO conditions together: the ray travels from a denser to a less dense medium AND the angle of incidence exceeds the critical angle.
- Diffraction
The spreading of a wave as it passes through a gap or around an obstacle. The spreading is greatest when the gap width is about equal to the wavelength (); a gap much wider than produces almost no noticeable spreading.
- Principle of superposition
When two or more waves meet, the resultant displacement at each point is the vector sum of the individual displacements. After overlapping, the waves pass through unchanged.
- Coherent sources
Sources that emit waves of the same frequency with a constant phase difference. Coherence is required for a stable, observable interference pattern.
- Path difference
The extra distance one wave travels compared with the other to reach a given point. Constructive interference: path difference . Destructive interference: path difference , with
- Young's double-slit fringe spacing
, where is the spacing between adjacent bright fringes, the wavelength, the slit-to-screen distance and the slit separation. Valid when .
- Diffraction grating equation (HL)
, where is the spacing between adjacent slits, the angle of the -th order maximum and A grating gives sharper, brighter maxima than two slits, ideal for spectroscopy.
- Single-slit first minimum (HL)
The first dark minimum of a single-slit diffraction pattern lies at (in radians), where is the slit width. The central maximum is twice as wide as the secondary maxima.
Name it
Read the meaning, then pick which of this lesson’s terms it describes. Miss one and you see what your choice really means.
, where is the spacing between adjacent bright fringes, the wavelength, the slit-to-screen distance and the slit separation. Valid when .
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
Angle of incidence = angle of reflection, both measured from the normal.
The incident ray, reflected ray and normal are coplanar.
Reflection occurs at every boundary — even one that mostly transmits light still reflects a little.
A rough surface reflects each ray by the same law but in scattered directions (diffuse reflection); a smooth surface gives a clear image (specular reflection).
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Get a Paper 2 calculation marked: solve a refraction or interference problem with full working
Get a Paper 2 calculation marked: solve a refraction or interference problem with full working
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do Get a Paper 2 calculation marked: solve a refraction or interference problem with full working on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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