Reflection and Refraction of Waves
Australia's NBN fibre-to-premises network delivers data at $0.67c$ (200,000 km/s) through Corning SMF-28 optical fibre: core refractive index $n_{core} = 1.4677$, cladding $n_{clad} = 1.4640$, critical angle $\theta_c = 86.9°$. Every data pulse stays trapped inside the glass core because each time it hits the core-cladding boundary it refracts — and if the angle exceeds 86.9°, all light reflects back internally. Reflection and refraction at a boundary are two aspects of the same phenomenon, and both are essential to fibre-optic communication.
When a wave travels from shallow water into deep water, the wave speed increases. Which way will the wavefront bend — towards the normal or away from it? Predict and explain.
Warm-up — angles in reflection are measured from:
Know
- Law of reflection: $\theta_i = \theta_r$
- Refraction changes wave speed and direction at a boundary
- Frequency is unchanged during refraction
Understand
- Why waves reflect off boundaries
- Why waves bend when they enter a new medium at an angle
- The relationship between speed, wavelength and direction change
Can Do
- Draw reflection and refraction diagrams with correct angle notation
- Predict refraction direction from speed information
- Apply reflection and refraction to real contexts
Core Content
Stand in a bathroom and clap sharply once — you hear the echo a fraction of a second later as sound bounces off the hard tiled walls. Aim a torch at a bathroom mirror at an angle — the reflected beam leaves at exactly the same angle on the other side of the perpendicular. Both the sound echo and the light beam are obeying the same law: the angle the wave arrives equals the angle it leaves, measured from the perpendicular to the surface (the normal).
When a wave hits a boundary it bounces off. The angle of incidence equals the angle of reflection. Both angles are measured from the normal to the boundary at the point of contact.
$\theta_i = \theta_r$
This holds for all wave types — water waves in a ripple tank, sound echoes, light in a mirror, and radar. The frequency, wavelength and speed of the reflected wave are identical to the incident wave.
The law of reflection states $\theta_i = \theta_r$ (both measured from the normal to the surface). Frequency, wavelength and speed are unchanged on reflection.
Pause — copy the highlighted law into your book before moving on.
A wave hits a boundary at 30° to the normal. The reflected ray makes an angle of __ with the normal:
We just saw that reflection preserves all wave properties and bounces the wave at equal angles. That raises a question: what happens if the wave enters the new medium rather than bouncing off? This card answers it → refraction changes speed and bends direction, but frequency stays constant.
When a wave enters a new medium at an angle, the change in speed causes the wavefront to bend. The side of the wavefront that enters the new medium first is the first to change speed, rotating the whole wavefront.
- Into a slower medium (e.g. deep water → shallow, air → glass): wave bends towards the normal.
- Into a faster medium (e.g. shallow water → deep, glass → air): wave bends away from the normal.
Refraction: a wave changes speed (and wavelength) when entering a new medium; it bends towards the normal when slowing down and away when speeding up. Frequency is invariant during refraction — it is set by the source.
Add the highlighted refraction rule to your notes before the check below.
When light refracts from air into glass, its frequency increases.
A wave entering a slower medium bends toward the normal.
Activities
Draw and label a reflection diagram for a wave arriving at 40° to the surface. Mark the normal, $\theta_i$ and $\theta_r$. State the angle of reflection.
For each scenario, state whether the wave bends toward or away from the normal when it enters the new medium:
- Air → glass (light slows)
- Deep water → shallow water (waves slow)
- Glass → air (light speeds up)
- Shallow water → deep water (waves speed up)
A wave of frequency 500 Hz travels from air (speed 340 m/s) into water (speed 1480 m/s). Find: (a) wavelength in air, (b) wavelength in water, (c) frequency in water.
Which of the following does NOT change when a wave refracts into a new medium?
A wave travels from medium A into medium B and bends away from the normal. This tells you that:
A wave hits a smooth flat boundary at 0° to the normal (straight on). After reflection, it travels:
UnderstandBand 3(3 marks) 1. State the law of reflection and explain why frequency and wavelength do not change when a wave reflects from a boundary.
ApplyBand 4(3 marks) 2. A 200 Hz wave travels from medium A (speed 200 m/s) into medium B (speed 400 m/s). State the frequency, calculate the wavelength in each medium, and identify which way the wavefront bends.
AnalyseBand 5(4 marks) 3. Radio waves entering the ionosphere slow down and refract back toward Earth. Explain this process using the concept of refraction and state the practical benefit.
Show all answers
Short Answer — Model Answers
Q1 (3 marks): The angle of incidence equals the angle of reflection ($\theta_i = \theta_r$), both measured from the normal. Frequency and wavelength do not change because the wave remains in the same medium; the boundary simply reverses the direction component perpendicular to it.
Q2 (3 marks): Frequency = 200 Hz (unchanged by refraction). $\lambda_A = 200/200 = 1$ m. $\lambda_B = 400/200 = 2$ m. Speed increases so the wave bends away from the normal.
Q3 (4 marks): At the boundary between the lower atmosphere and the ionosphere, wave speed decreases. The side of the wavefront entering the slower region first is slowed, causing the wavefront to rotate towards the normal. Progressively, the wave bends back toward Earth. Practical benefit: long-range HF radio communication without satellites, reaching over-the-horizon locations.
Australia's NBN fibre-to-premises network makes the lesson concrete: the glass core ($n = 1.4677$) is only slightly denser than the cladding ($n = 1.4640$), yet that tiny difference is enough that light entering the core refracts at the boundary. When the angle of incidence exceeds the critical angle of 86.9°, all light reflects back internally and data travels at $0.67c$ across the 12,000 km Sydney–Los Angeles cable. Your Think First question was about refraction direction: when a wave enters a faster medium (lower $n$), it bends away from the normal — the wavefront's leading edge speeds up, rotating the whole front outward.