Theme C — Wave Behaviour
C.3.1 Wavefronts and Rays — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 17 of 37 1 quiz
Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
Lesson summary
C.3.1 Wavefronts and Rays — IB PHYSICS SL notes: Represent waves with wavefronts and rays and use them to describe plane, circular and spherical waves and the Huygens construction.Surface wave — it travels in two dimensions and has circular wavefronts, such as ripples on waterSph…
- Distinction
- Plane wavefront
- Drawing peaks and troughs
- Viewed from above
- Choice of diagram
- Slower medium
Part 1 of 7Dimensions of waves
Surface wave
- Surface wave it travels in two dimensions and has circular wavefronts, such as ripples on water
Spherical wave
- Spherical wave it travels in three dimensions and has spherical wavefronts, such as sound or light from a point source
Distinction
- Distinction a circle is a 2D shape and a sphere is a 3D shape
Plane wavefront
- Plane wavefront far from a source a small part of a spherical wavefront is effectively flat
- A long straight vibrating bar in a ripple tank produces plane waves.
- A distant source such as the Sun does too.
Part 2 of 7Wavefronts
1Wavefront
- Wavefront a line (2D) or surface (3D) joining all points of a wave that oscillate in the same phase
- It is perpendicular to the direction of motion and energy transfer.
2Spacing
- Spacing wavefronts drawn through successive crests are one wavelength apart
3Drawing peaks and troughs
- Drawing peaks and troughs peaks are often drawn darker and troughs fainter, and some diagrams show only peak wavefronts
4Viewed from above
- Viewed from above a plane wave looks like a series of parallel lines
Part 3 of 7Rays
Ray
- Ray a line showing the direction in which the wave energy travels
Direction
- Direction in a uniform isotropic medium a ray is always at right angles to the wavefronts
Patterns
- Patterns rays from a point source diverge radially, rays of a plane wave are parallel, and rays converge towards a focus after a lens or curved mirror
Choice of diagram
- Choice of diagram ray diagrams suit reflection and refraction because they track direction
- Wavefront diagrams suit refraction and diffraction because the spacing shows the wavelength.
Part 4 of 7Wavefront spacing, speed and wavelength
Speed
- Speed wavefronts travel at the wave speed v
Spacing
- Spacing the distance between neighbouring wavefronts is λ, and the time between wavefronts passing a point is T
Slower medium
- Slower medium the frequency stays the same, so the wavefronts crowd closer together
- λ decreases in proportion to v (v = fλ).What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
- This causes the change of direction at a boundary.
Intensity
- Intensity spherical wavefronts of radius r spread the power over area 4πr2, so intensity falls as 1/r2 and amplitude as 1/r
Part 5 of 7Huygens' construction
Principle
- Principle every point on a wavefront acts as a source of secondary spherical wavelets with the same speed and frequency as the original wave
New wavefront
- New wavefront after time t it is the common tangent (envelope) of all the wavelets, whose radii are each vt
- A flat wavefront gives a flat new wavefront.
- A circular wavefront gives an enlarged circle.
At a gap
- At a gap only points within the gap emit wavelets, so the wave spreads into the shadow region, which is diffraction
At a boundary
- At a boundary the wavelets travel different distances in the same time, so the envelope tilts, which is refraction
Interference
- Interference the method also explains patterns from several slits
Part 6 of 7Drawing wavefront diagrams
Uniform medium
- Uniform medium draw wavefronts equally spaced, with spacing equal to the wavelength
Rays
- Rays draw them perpendicular to the wavefronts with arrows for the direction
Slower region
- Slower region make the spacing smaller there
Gap
- Gap draw wavefronts with the same spacing but curving at the edges, with more spreading when the gap is comparable to the wavelength
Angles
- Angles label the angle between a ray and the normal, never the angle to the wavefront
Equipment
- Equipment use a ruler for straight lines
Constants
- Constants state that frequency is constant while speed and wavelength change
Part 7 of 7More from the specification
More from the specification
Snell's Law and Refractive Index
- When a wave passes across a boundary between two transparent media, the angle of incidence θ_1 and angle of refraction θ_2 satisfy the refraction equation n1 sin(θ_1) = n2 sin(θ_2),
- where n represents the refractive index of the material.
Critical Angle and Total Internal Reflection
- Total internal reflection occurs when an incident light ray within an optically denser medium strikes the boundary at an angle exceeding the critical angle c,
- where sin(c) = 1 / n.
Wavefronts and Ray Direction
- Rays indicate the direction of wave propagation and are always perpendicular to wavefronts as they encounter an aperture, reflecting surface,
- or refracting boundary.
Double-Source Interference Patterns
- When coherent wavefronts overlap, constructive interference occurs at points of zero path difference or integer wavelengths (n λ),
- whereas destructive interference occurs when path difference is (n + 1/2) λ.
Snell's Law and Refractive Index
- When a wave passes across a boundary between two transparent media, the angle of incidence θ_1 and angle of refraction θ_2 satisfy the refraction equation n1 sin(θ_1) = n2 sin(θ_2),
- where n represents the refractive index of the material.
Critical Angle and Total Internal Reflection
- Total internal reflection occurs when an incident light ray within an optically denser medium strikes the boundary at an angle exceeding the critical angle c,
- where sin(c) = 1 / n.
Wavefronts and Ray Direction
- Rays indicate the direction of wave propagation and are always perpendicular to wavefronts as they encounter an aperture, reflecting surface,
- or refracting boundary.
Double-Source Interference Patterns
- When coherent wavefronts overlap, constructive interference occurs at points of zero path difference or integer wavelengths (n λ),
- whereas destructive interference occurs when path difference is (n + 1/2) λ.
Critical angle
- Incline angle at which sliding just begins.
Optically dense
- Having a high refractive index
Destructive
- Waves in antiphase giving reduced amplitude.
Superposition
- Resultant displacement is the sum of the displacements of the individual waves.
Coherent
- Constant phase difference and same frequency.
Transmission
- Sending electricity along power cables from the power station to consumers.
n1 sin θ1
n1 sin θ1 n2 sin θ2
What the symbols mean: n = refractive index (no unit) · i or θ1 = angle of incidence · r or θ2 = angle of refraction (both measured from the normal)
Key terms
| Term | Meaning |
|---|---|
| Wavefront | Line or surface joining points in the same phase. |
| Ray | Line showing the direction of energy transfer, perpendicular to wavefronts. |
| Plane wave | Wave whose wavefronts are parallel flat surfaces. |
| Huygens' principle | Each point on a wavefront is a source of secondary wavelets. |
| Wavelet | Secondary circular or spherical wave from a point on a wavefront. |
Avoid these mistakes
1
Drawing rays parallel to wavefronts — rays are always perpendicular to them.
2
Spacing wavefronts equally in two different media — wavelength changes when the speed changes.
3
Thinking plane wavefronts need a plane source — any distant point source gives approximately plane waves.
4
Forgetting that Huygens' wavelets have the same speed and frequency as the parent wave.
5
Measuring angles from the wavefront instead of the normal.
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