IB DP Physics: Wavefronts, rays, reflection, refraction and diffraction (DP Physics) – Revision Notes

These notes condense the first half of sub-topic C.3 (Wave phenomena) in the IB Physics guide, first assessment 2025. Everything here is SL and HL. Interference, single-slit diffraction and gratings are covered elsewhere in C.3. For full explanations and derivations use the study guide, and test yourself with the practice questions. Also see the course hub, the printable checklist and travelling waves and the Doppler effect. To find gaps first, take the free 10-minute diagnostics.

Definitions

Term	Meaning
Wavefront	Line (2D) or surface (3D) joining points at the same phase
Ray	Line showing the direction of travel and energy transfer; perpendicular to wavefronts
Normal	Line at 90° to the boundary, used to measure every angle
Reflection	Wave bounces back into the first medium
Transmission	Wave passes into the second medium
Refraction	Change of direction caused by a change of speed at a boundary
Diffraction	Spreading of a wave through an aperture or round a body
Critical angle C	Angle of incidence in the denser medium that gives a refracted angle of 90°
Total internal reflection	All of the wave is reflected because the angle of incidence exceeds C

Wavefront shapes

• Point source, 2D: circular wavefronts, rays radiate outwards.
• Point source, 3D: spherical wavefronts.
• Distant source: wavefronts look flat and rays look parallel.
• Wavefront spacing is one wavelength.

Key relationships

Idea	Statement
Reflection	Angle of incidence = angle of reflection, both from the normal
Snell’s law (guide form)	n1 / n2 = sin θ2 / sin θ1 = v2 / v1
Working form	n1 sin θ1 = n2 sin θ2
Refractive index and speed	n = c / v
Wave equation	v = f λ
Critical angle	sin C = n2 / n1, with n1 > n2

What changes at a boundary

Quantity	Reflection	Refraction
Frequency	Same	Same
Speed	Same	Changes
Wavelength	Same	Changes with speed
Direction	Reverses (angle in = angle out)	Changes unless incident along the normal

Slower medium (higher n): wavefronts closer together, ray bends towards the normal. Faster medium (lower n): wavefronts further apart, ray bends away from the normal.

Method: a refraction calculation

1. Mark the angles from the normal. If you are given an angle to the surface, subtract it from 90°.
2. Write n1 sin θ1 = n2 sin θ2, or sin θ2 / sin θ1 = v2 / v1 for waves given as speeds.
3. Rearrange for the unknown sine, then use the inverse sine.
4. Check direction: into a higher n, the angle gets smaller.
5. For wavelength, keep the frequency fixed: λ2 = λ1 × (v2 / v1) = λ1 × (n1 / n2).

Small reminder. Light of wavelength 650 nm in air enters glass of refractive index 1.60. The speed becomes 3.00 × 10⁸ / 1.60 = 1.88 × 10⁸ m s⁻¹ and the wavelength becomes 650 / 1.60 = 406 nm. The frequency has not changed.

Method: total internal reflection

1. Check that the wave is going from higher n to lower n. If not, there is no critical angle.
2. Work out sin C = n2 / n1 and C.
3. Compare the angle of incidence with C. Above C means total internal reflection; below C means partial reflection and a refracted ray.
4. If the angle of incidence equals C, the refracted ray travels along the boundary.

Small reminder. For a wave going from a medium of n = 1.45 into one of n = 1.20, sin C = 1.20 / 1.45 = 0.8276, so C = 55.9°.

Method: drawing a wavefront-ray diagram

1. Draw the boundary and the normal, then the incident rays at the stated angle to the normal.
2. Draw incident wavefronts perpendicular to the rays, equally spaced by one wavelength.
3. For refraction, draw the wavefronts in medium 2 with a new spacing: closer in a slower medium, further apart in a faster one. The wavefronts must meet the boundary where the incident ones do, with no gaps or breaks.
4. Draw the rays in medium 2 perpendicular to the new wavefronts. Check that the bend matches Snell’s law.
5. For diffraction, keep the spacing of the wavefronts unchanged and curve them into the shadow, more strongly for a narrow gap.

Small reminder. Ripples go from deep water to a shelf where the speed halves. The wavelength halves too, because the frequency is fixed, so the wavefront spacing on the shelf is half the spacing in deep water.

Diffraction in brief

Situation	What you see
Gap much wider than λ	Wave passes with little spreading; clear shadow either side
Gap about the same as λ, or smaller	Strong spreading; near-circular wavefronts beyond the gap
Small body, size close to λ	Wave bends round and fills in much of the shadow
Large body, size much greater than λ	Sharp shadow

Speed, wavelength and frequency do not change on diffraction. The wavefront shape and the spread do.

Must-know distinctions

• Reflection vs refraction: reflection stays in medium 1; refraction enters medium 2 and changes speed.
• Refraction vs diffraction: refraction needs a change of medium; diffraction can happen in a single medium and needs an aperture or edge.
• Partial vs total reflection: partial happens at any angle; total only above C and only going into a lower n.
• Ray vs wavefront angles: the angle between ray and normal equals the angle between wavefront and boundary.

Quick self-test

1. What is the angle between a ray and the wavefronts it crosses, and what does the ray show?
2. A ray meets a plane mirror at 20° to the surface. Give the angle of reflection and the angle between the incident and reflected rays.
3. Which of frequency, speed and wavelength change when a wave refracts?
4. Light in air meets water (n = 1.33) at 25.0° to the normal. Find the angle of refraction.
5. Light of wavelength 650 nm in air enters glass with n = 1.60. State the speed and wavelength in the glass.
6. Light travels at 2.25 × 10⁸ m s⁻¹ in a liquid. Find its refractive index.
7. Water waves travel at 0.40 m s⁻¹ in deep water and 0.30 m s⁻¹ in shallow water. Their rays meet the boundary at 30° to the normal. Find the angle of refraction.
8. Explain why a critical angle does not exist for light going from air into glass.
9. A ray in glass (n = 1.60) meets a glass-air boundary at 38° to the normal. Does it emerge, and at what angle?
10. A diver’s torch beam inside a pool reaches the surface at 55° to the normal. Does it escape into the air? (Use n = 1.33 for water.)
11. Waves of wavelength 2 cm and of wavelength 0.5 cm each pass through a 3 cm gap. Which spreads more, and why?

Answers

1. 90°. The ray shows the direction of travel and energy transfer.
2. Angle of incidence = 90° − 20° = 70°, so the angle of reflection is 70°. The angle between the rays is 140°.
3. Speed and wavelength change. Frequency does not.
4. sin θ2 = sin 25.0° / 1.33 = 0.4226 / 1.33 = 0.3177, so θ2 = 18.5°.
5. v = 3.00 × 10⁸ / 1.60 = 1.88 × 10⁸ m s⁻¹. λ = 650 / 1.60 = 406 nm.
6. n = c / v = 3.00 × 10⁸ / 2.25 × 10⁸ = 1.33.
7. sin θ2 = (0.30 / 0.40) × sin 30° = 0.75 × 0.5 = 0.375, so θ2 = 22.0°.
8. Light is going from a lower n to a higher n, so it bends towards the normal. The sine of the refracted angle can never reach 1, so there is no refracted angle of 90°.
9. C = sin⁻¹(1.00 / 1.60) = 38.7°. The angle 38° is below C, so the ray emerges. sin θ2 = 1.60 × sin 38° = 0.985, so θ2 = 80.1°. Some light is also reflected.
10. C = sin⁻¹(1.00 / 1.33) = 48.8°. The angle 55° is greater than C, so there is total internal reflection and no light escapes.
11. The 2 cm waves spread more, because their wavelength is closer to the gap width. The 0.5 cm waves pass with less spreading.

Where marks are usually lost

• Measuring angles from the surface instead of from the normal.
• Using sin C = n1 / n2, or putting the refractive indices the wrong way round in Snell’s law.
• Changing the frequency when finding the new wavelength.
• Writing “bends towards the normal” for a ray going into a faster medium.
• Giving a calculated sine greater than 1 as an angle without noticing that total internal reflection applies.
• Calling the effect refraction when the question describes spreading through a gap, which is diffraction.
• Drawing refracted wavefronts the same distance apart as the incident ones, or not perpendicular to the rays.
• Saying total internal reflection happens “when light goes from dense to less dense” without giving the angle condition.
• Rounding too early. Keep the sine to four figures until the end.

Official syllabus

IB Physics guide, first assessment 2025, published by the International Baccalaureate Organization: sub-topic C.3 Wave phenomena (first half of the understandings).