Reflection, Refraction and Diffraction of Waves

Waves do three things at boundaries and gaps: reflect, refract and diffract. Cambridge tests all three with ripple-tank wavefront diagrams, and the marks sit in the details: what changes, what stays the same, and how the wavefronts bend.

What happens to a wave during reflection, refraction and diffraction?

Behaviour	What happens	What changes	What stays the same
Reflection	Wave bounces off a barrier	Direction	Speed, wavelength, frequency
Refraction	Wave changes direction entering a new medium/depth	Speed, wavelength, direction	Frequency
Diffraction	Wave spreads out through a gap or around an edge	Direction (spreading)	Speed, wavelength, frequency

One rule governs every row: frequency never changes. The source sets the frequency, and nothing at a boundary can alter it. State that whenever a question asks what happens to frequency.

In a ripple tank, reflection obeys the same law as light: angle of incidence equals angle of reflection, both measured from the normal. Refraction is modelled with a submerged plastic sheet creating shallow water. Waves travel slower in shallow water, so the wavelength shortens, and wavefronts crossing the boundary at an angle bend towards the normal. Speed change is the cause of refraction, so name it explicitly.

How does gap size affect diffraction?

This is the Extended (Supplement) detail. Maximum diffraction happens when the gap width is similar to the wavelength: the wave emerges as near-semicircular wavefronts. When the gap is much wider than the wavelength, the wave passes through almost straight, spreading only slightly at the edges. Longer wavelengths diffract more around the same obstacle. That is why sound (wavelength around 1 m) bends around a doorway but light (wavelength around $5 \times 10^{-7}\ \text{m}$) does not, and why long-wavelength radio signals reach behind hills.

Worked Exam Question

Plane water waves of wavelength 4 cm travel at 20 cm/s towards a boundary into shallower water, where their speed falls to 15 cm/s. (a) Calculate the frequency of the waves. [2] (b) Calculate the new wavelength in the shallow water. [2]

Worked solution:

1. (a) Equation: $v = f\lambda$, so $f = v \div \lambda$
2. Substitute: $f = 20 \div 4 = 5.0\ \text{Hz}$
3. (b) Frequency is unchanged at the boundary. Rearrange: $\lambda = v \div f$
4. Substitute: $\lambda = 15 \div 5.0 = 3.0\ \text{cm}$ (2 significant figures)

Mark scheme:

• M1: $f = v \div \lambda$ or correct substitution $20 \div 4$
• A1: $5.0\ \text{Hz}$
• M1: uses unchanged frequency: $\lambda = 15 \div 5.0$ (error carried forward allowed)
• A1: $3.0\ \text{cm}$ with unit

Common Mistakes

• Changing the frequency during refraction. Frequency is fixed by the source; only speed and wavelength change.
• Drawing refracted wavefronts with the same spacing. Slower water means shorter wavelength, so draw the wavefronts closer together in the shallow region.
• Measuring angles from the surface instead of the normal. Every angle in this topic is measured from the normal.
• Drawing diffraction through a wide gap as full semicircles. Wide gaps give mostly straight wavefronts with curvature only at the edges.
• Mixing up diffraction with refraction. Diffraction needs a gap or edge; refraction needs a change of medium or depth.

Exam Technique Tip

For wavefront diagrams, count and copy the spacing. Keep the same number of wavefronts on each side of a barrier for reflection and diffraction, and deliberately shrink the spacing on the slow side for refraction. Use a pencil and ruler for straight wavefronts and keep curves smooth. Cambridge awards diagram marks for spacing and shape, not artistic quality.

How This Is Examined

All papers carry this subtopic. Papers 1 and 2 use wavefront pictures: pick the correct diffraction pattern, or identify what stays constant during refraction. Papers 3 and 4 ask you to complete wavefront diagrams and run calculations like the worked example; the gap-size and wavelength dependence of diffraction is Extended-only, so Core candidates just describe spreading through a gap. The ripple tank is a named piece of apparatus, so Papers 5 and 6 can ask how to measure wavelength or speed in one. Wavefront diagrams are hard to visualise from a textbook. In online 1-to-1 classes we draw them live on a shared whiteboard until the patterns stick, usually within one session.