Reflection sends a wave back with its angle preserved
Definition
Reflection
The bouncing back of a wave when it meets a barrier, so that it stays in the same material instead of crossing into a new one.
- Send straight wavefronts at a flat barrier placed at an angle and they bounce off it as straight wavefronts travelling in a new direction.
- Draw a normal, a construction line at 90∘90^\circ90∘ to the barrier where the wave strikes it, and measure both angles from that line.
- The angle of incidence always equals the angle of reflection, which is why a wave arriving at 30∘30^\circ30∘ leaves at 30∘30^\circ30∘ on the other side of the normal.
- Nothing about the wave itself changes on reflection: the speed, frequency and wavelength all stay the same, because the wave is still in the same water.
- Only the direction of travel changes, so on a wavefront diagram the spacing of the lines is unchanged and only their angle is different.
- This is the behaviour behind an echo off a cliff and behind the image you see in a mirror.
Refraction bends a wave because its speed changes
Definition
Refraction
The change in direction of a wave as it crosses a boundary into a new region, caused by a change in its speed.
- Water waves travel more slowly in shallow water than in deep water, so a submerged glass plate creates a shallow region where the speed drops.
- The source is still vibrating at the same rate, so the frequency cannot change as the wave crosses the boundary.
- With v=fλv = f\lambdav=fλ and fff fixed, a smaller vvv forces a smaller λ\lambdaλ, so the wavefronts bunch closer together in the shallow region.
- If the wave meets the boundary at an angle, one end of each wavefront reaches the shallow water and slows down before the other end does.
- That lagging end pivots the whole wavefront round, so the wave changes direction and bends towards the normal on entering the slower region.
- Going back into deep water the wave speeds up again and bends away from the normal.
- If the wavefronts arrive parallel to the boundary, every point slows at the same instant, so the wavelength still shortens but the direction does not change at all.
- This is why sea waves swing round to run almost parallel to a beach: the end of each wave that reaches the shallows first is slowed and held back.
Diffraction spreads a wave out past a gap or an edge
Definition
Diffraction
The spreading out of a wave as it passes through a gap or travels past the edge of an obstacle.
- Put two barriers in the tank with a gap between them and send straight wavefronts at the gap.
- A narrow gap, roughly as wide as one wavelength, turns the straight wavefronts into curved ones that fan out into almost the whole region beyond.
- A wide gap lets most of the wave through unchanged, with only the two ends curling round, so the beam stays roughly the width of the gap.
- Replace the gap with a single barrier and the wave curls round its edge into the shadow region behind it, so the water there is not perfectly still.
- Diffraction changes only the shape and direction of the wavefronts, because the water is the same depth throughout and so the speed, frequency and wavelength are all unchanged.
- It explains why you can hear someone talking round a doorway even though you cannot see them: sound has a wavelength close to the width of the door, while light does not.
Practical
Investigation: reflection, refraction and diffraction in a ripple tank
- Note: this is normally set up and run by the teacher as a class demonstration, but you still need to be able to describe the method and the result.
- Aim: to show the reflection, refraction and diffraction of water waves and to see how the wavefronts change in each case.
- Apparatus: a ripple tank with a motorised straight vibrating bar, a lamp above the tank and a white screen below it, a stroboscope, straight metal barriers, a flat glass plate and a ruler.
- Method:
- Level the tank and fill it with water to a depth of about 1 cm1\ \text{cm}1 cm, then switch on the lamp so the crests act as lenses and throw bright lines onto the screen beneath.
- Lower the vibrating bar until it just touches the surface and run the motor slowly to send straight wavefronts down the tank.
- View through a stroboscope and adjust its rate until the pattern appears frozen, which makes the wavefronts easy to sketch and measure.
- Reflection: stand a straight barrier across the tank at about 45∘45^\circ45∘ to the oncoming wavefronts and sketch the incident and reflected wavefronts, marking the normal and both angles.
- Refraction: remove the barrier and lay the flat glass plate on the floor of the tank to make a shallow region, first with its edge parallel to the wavefronts and then turned at an angle, sketching the wavefronts each time.
- Diffraction at a gap: take the plate out, set two barriers to leave a gap about one wavelength wide, sketch the pattern beyond it, then widen the gap to several wavelengths and sketch it again.
- Diffraction at an edge: remove one barrier so a single straight edge is left, and sketch how the wavefronts curl into the shadow behind it.
- Measure and plot:
- Measure the angles of incidence and reflection from the sketch with a protractor.
- Find the wavelength in the deep and the shallow water by measuring across ten wavefront spacings and dividing by ten.
- Result: the angle of reflection equals the angle of incidence; in the shallow region the wavefronts are closer together and are turned towards the normal; a gap of about one wavelength spreads the wave strongly while a wide gap barely spreads it, and a single edge lets the wave curl into the shadow.
- Watch out:
- Moving wavefronts are almost impossible to measure by eye, so use the stroboscope or photograph the pattern rather than guessing.
- Keep the water shallow and the tank level, because a sloping tank changes the depth across the tank and refracts the waves where you did not intend it to.
- Waves reflecting off the far wall run back into the pattern, so fit sloping gauze or foam edges to absorb them.
- Safety: flashing stroboscope light can trigger a seizure in a person with photosensitive epilepsy, so the class is asked first, and any water spilt near the electrical supply is mopped up straight away.
Only refraction changes the wavelength, and nothing changes the frequency
- The frequency is fixed by the vibrating bar, so nothing that happens inside the tank can alter it in any of the three effects.
- Reflection and diffraction both leave the wave in water of the same depth, so the speed and wavelength are untouched and only the direction or shape of the wavefronts changes.
- Refraction is the only one of the three that moves the wave into water of a different depth, so it is the only one that changes the speed and therefore the wavelength.
- That makes the spacing of the wavefronts the single most informative thing on any wavefront diagram, because a change in spacing can only mean refraction.
- All three effects can happen to any wave, not just water waves, which is why the ripple tank is used as a model for light and sound as well.
Common Mistake
- Do not say the frequency changes when a wave is refracted, because the source sets the frequency and it survives the boundary unchanged.
- Do not claim a wave always bends when it is refracted; hitting the boundary head-on shortens the wavelength but leaves the direction alone.
- Do not draw the diffracted wavefronts closer together or further apart, because diffraction does not change the wavelength.
- Do not measure angles from the barrier itself; every angle is measured from the normal.
- Do not explain refraction as "the wave bends" and stop there; the mark is for the change in speed that causes the bending.
Exam technique
- Working out which effect a wavefront diagram is showing:
- Check the spacing of the wavefronts first, because only refraction changes it.
- Straight wavefronts, unchanged spacing and a new direction after a barrier means reflection.
- Closer spacing and a new direction after a depth change means refraction.
- Curved wavefronts fanning out past a gap or an obstacle, with the spacing unchanged, means diffraction.
- When you are asked to complete a wavefront diagram, keep your lines evenly spaced and parallel, because sloppy spacing loses the mark even when the idea is right.
- Describing the ripple tank is point-marked, so name the barrier or glass plate, the stroboscope and what you sketch, rather than writing "we looked at the waves".
- For refraction, always give the chain: the depth changes, so the speed changes, so the wavelength changes, so the direction changes.
- The mark most often dropped in a diffraction answer is the comparison, so say the spreading is greatest when the gap is about the same size as the wavelength.
Self review
- What happens to the speed, frequency and wavelength of a wave when it reflects off a plane barrier?
- Explain why a water wave changes direction when it crosses into shallower water at an angle.
- Describe how a ripple tank is used to demonstrate refraction.
- Sketch the wavefronts beyond a narrow gap and beyond a wide gap, and say how they differ.
- Which of the three effects changes the wavelength, and why do the other two not?
