Reflection Refraction and Doppler Effect
This topic covers the fundamental behaviours of waves when they encounter a surface or boundary. It explains reflection, refraction, and the Doppler effect, focusing on how wave properties like speed, frequency, and wavelength are affected.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- During reflection, a wave bounces off a surface. The angle of incidence equals the angle of reflection. The wave's speed, frequency, and wavelength remain unchanged as it stays in the same medium.
- During refraction, a wave passes from one medium into another, causing its speed to change. This change in speed causes the wave to bend, unless it strikes the boundary along the normal.
- Frequency is the only wave property that remains constant during refraction. The rate of wavefronts arriving at a boundary must equal the rate leaving it.
- If a wave slows down entering a new medium, it bends towards the normal and its wavelength decreases. If it speeds up, it bends away from the normal and its wavelength increases.
- The Doppler effect describes the change in observed frequency when there is relative motion between a wave source and an observer. Moving towards each other increases frequency; moving apart decreases it.
Diagrams
› Why does this happen?
Why a wave bends: The marching soldiers analogy
Imagine a line of soldiers marching in step from hard pavement onto thick mud at an angle. The first soldier to reach the mud slows down, while the others still on the pavement keep the faster pace.
This makes the whole line pivot and change direction.
A wavefront behaves the same way: the part that enters the slower medium first slows down, so the whole wavefront bends towards the normal.
Two things stay the same and one changes:
- The frequency stays constant - the number of wavefronts arriving at the boundary each second equals the number leaving it.
- Because the wave now travels slower at the same frequency, the wavefronts bunch up, so the wavelength decreases.
Why the Doppler effect happens: Squeezing the waves
Think of a stationary ambulance emitting sound. The wavefronts spread outwards as evenly spaced circles.
Now let the ambulance move towards you. After it emits one wavefront it moves forward before emitting the next, so each new wavefront starts from a point closer to you.
This squashes the wavefronts together in front of the ambulance, decreasing the wavelength.
The speed of sound in air is constant, and v = f × λ, so:
- In front (source moving towards you): a shorter wavelength means a higher frequency - a higher pitch.
- Behind (source moving away): the wavefronts are stretched out, giving a longer wavelength and a lower pitch.
Formulae
v = f × λ The fundamental wave equation, relating wave speed (v), frequency (f), and wavelength (λ). Crucial for understanding why wavelength must change when speed changes during refraction (as frequency is constant).
i = r The Law of Reflection. Use this to determine the path of a reflected wave. 'i' is the angle of incidence and 'r' is the angle of reflection.
Definitions
- Normal
- An imaginary line drawn at a right angle (90°) to a surface or boundary at the point where a wave makes contact. All key angles are measured from this line.
- Angle of Incidence (i)
- The angle between the direction of the incoming wave and the normal.
- Reflection
- The bouncing back of a wave from a surface. The law of reflection states that the angle of incidence equals the angle of reflection.i = r
- Refraction
- The change in direction of a wave as it passes from one medium to another, caused by a change in the wave's speed.
Worked example
A boat uses sonar to measure the depth of the sea. It sends a sound pulse downwards and detects the reflected echo 0.2 seconds later. The speed of sound in seawater is 1500 m/s. The boat then moves to a shallower region where the echo is detected 0.1 seconds later. What is the difference in sea depth between the two locations?
- 1
Step 1:
Calculate the total distance travelled by the first pulse.
This is a round trip (down and back up).
Distance = speed × time = 1500 m/s × 0.2 s = 300 m - 2
Step 2:
The sea depth is half of this total distance.
Depth 1 = 300 m / 2 = 150 m - 3
Step 3:
Calculate the total distance travelled by the second pulse.
Distance = 1500 m/s × 0.1 s = 150 m - 4
Step 4:
The second sea depth is half of this new distance.
Depth 2 = 150 m / 2 = 75 m - 5
Step 5:
Find the difference in depth.
Difference = Depth 1 - Depth 2 = 150 m - 75 m = 75 m
Answer: 75 m
Common mistakes
- ×Incorrectly measuring angles from the surface of the material instead of from the normal. All angles (incidence, reflection, refraction) are defined relative to the line perpendicular to the boundary.
- ×Forgetting to account for the two-way journey of a wave in echo-location problems. The calculated distance using `d = v × t` is for the round trip; you must halve it to find the distance to the object.
- ×Mixing up which properties change. For reflection, only direction changes. For refraction, speed and wavelength change together, while frequency is always constant.
No-calculator tips
- ✓In echo problems, the numbers are often chosen to be simple. For `d = v × t`, if you need to multiply 1500 by 0.2, think of it as 1500 × (1/5) or (1500 × 2) / 10, which is 3000 / 10 = 300.
- ✓When comparing refraction scenarios, think in ratios. If a wave's speed is reduced to one-third of its original value upon entering a medium, its wavelength will also become one-third of its original value, as `v` is proportional to `λ` when `f` is constant.
- ✓Visualise the Doppler effect: a vehicle coming towards you 'squashes' the sound waves together, leading to a shorter wavelength and higher pitch. As it moves away, it 'stretches' them out, giving a longer wavelength and lower pitch.