Wave Phenomena

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Wavefronts & Rays

Wavefronts are lines joining all points that oscillate in phase and are perpendicular to the direction of motion and energy transfer.
Rays are lines showing the direction of motion and energy transfer of the wave, perpendicular to the wavefront.
A surface wave propagates in two dimensions and has circular wavefronts, like ripples on water.
A spherical wave propagates in three dimensions and has spherical wavefronts, such as sound or light.
The distance between successive peak wavefronts (or trough wavefronts) equals the wavelength of the waves.
In diagrams, peaks are often shown with a darker line and troughs with a fainter line; some diagrams show only peak wavefronts.

Reflection, Refraction & Transmission

When waves meet a boundary between two media, they can be reflected, refracted, transmitted or absorbed.
Reflection occurs when a wave bounces back into the original medium; the law of reflection states angle of incidence = angle of reflection.
The angle of incidence is measured between the incident ray and the normal (a line at 90° to the boundary).
Refraction is the change in direction of a wave when it crosses a boundary between media of different densities, caused by a change in wave speed.
When light passes from a less dense to a more dense medium (e.g. air → glass), it slows down, has a shorter wavelength, and bends towards the normal.
When light passes from a more dense to a less dense medium (e.g. glass → air), it speeds up, has a longer wavelength, and bends away from the normal.
During refraction, speed and wavelength change but frequency remains the same (the colour of light does not change).
Transmission is the general term for a wave passing through a substance; refraction is a type of transmission. During transmission, frequency and speed do not change, but amplitude may decrease if absorption occurs.

Reflection of light

Diffraction of Waves

Diffraction is the spreading out of waves after they pass through a narrow gap or around an obstruction.
Diffraction occurs when waves pass through an aperture or around a barrier.
Diffraction effects are most noticeable when the wavelength is similar in size to the gap width or barrier.
For gaps much smaller than the wavelength, the wave spreads out significantly; for gaps much bigger than the wavelength, there is little diffraction.
When a wave passes through a gap, its amplitude decreases because the barrier absorbs some wave energy.
When a wave goes past a barrier, the greater the wavelength, the greater the diffraction; shorter wavelengths undergo less diffraction.
For a barrier larger than the wavelength, there is some diffraction, a lot of reflection, and a 'shadow' region behind the barrier.
For a barrier smaller than the wavelength, no diffraction occurs around it and the 'shadow' region is very small.

Diffraction through a gap

$Diffraction through a gap$

Refraction of Waves

The refractive index n of a material tells us how optically dense it is; n = c / v, where c is the speed of light in a vacuum and v is the speed in the medium.
The refractive index of air is approximately n = 1; more optically dense media have n > 1.
The higher the refractive index, the more optically dense the material and the slower light travels through it.
Snell's law relates the angles of incidence and refraction to the refractive indices and speeds: n₁ sin θ₁ = n₂ sin θ₂, or n₁/n₂ = sin θ₂ / sin θ₁ = v₂ / v₁.
The critical angle θc is the angle of incidence for which the angle of refraction is exactly 90°; it is found using sin θc = n₂ / n₁.
The larger the refractive index of a material, the smaller its critical angle.
Total internal reflection occurs when the angle of incidence exceeds the critical angle and the refractive index of the first medium is greater than that of the second (n₁ > n₂).
Total internal reflection follows the law of reflection: angle of incidence = angle of reflection.

Refraction of light

$Refraction of light$

Superposition of Waves

Superposition occurs when two or more waves overlap at a point; the resultant displacement is the sum of the individual displacements.
The principle of superposition states that when waves overlap, the displacement at a point equals the algebraic sum of the displacements of the individual waves.
Individual wave displacements may be positive or negative and are combined like vector quantities.
When two pulses meet, the resultant displacement is the algebraic sum of their displacements; after interacting, they carry on as normal.
Superposition can be analysed using displacement–position or displacement–time graphs.

Interference of Waves

Interference is the effect observed due to the superposition of two or more waves.
Constructive interference occurs when waves meet in phase (peak-to-peak or trough-to-trough), producing a resultant wave of larger amplitude.
Destructive interference occurs when waves meet in antiphase (peak-to-trough), cancelling each other out.
For waves to be coherent, they must have the same frequency and a constant phase difference.
Path difference is the difference in distance travelled by two waves from their sources to the point where they meet.
Constructive interference occurs when path difference = nλ (n = 0, 1, 2, ...).
Destructive interference occurs when path difference = (n + ½)λ (n = 0, 1, 2, ...).
On a wavefront diagram, count the number of wavelengths from each source to a point to determine the path difference and hence the type of interference.

Young's Double-Slit Experiment

Young's double-slit experiment produces a diffraction and interference pattern using a single wave source passing through a double slit.
Lasers are commonly used because the light must be coherent (constant phase difference and frequency) and monochromatic (single wavelength).
The light source is placed behind a single slit; light diffracts to produce two coherent sources at the double slit, which then diffract to form an interference pattern on a screen.
The pattern consists of bright fringes (maxima) from constructive interference and dark fringes (minima) from destructive interference.
Each bright fringe is identical in width and intensity; each dark fringe has zero intensity.
The double-slit equation gives the fringe spacing: s = λD / d, where s is the separation between successive fringes, λ is the wavelength, D is the distance from slits to screen, and d is the slit separation.
The fringe spacing s increases if the wavelength increases, the screen distance D increases, or the slit separation d decreases.
The order n of a maximum or minimum represents its position away from the central maximum: n = 0 is the central maximum, n = 1 the first maximum on either side, and so on.

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1.Which statement defines a wavefront?
Easy
- AA line joining all points that oscillate in phase, perpendicular to the direction of energy transfer
- BA line showing the direction of motion and energy transfer of the wave
- CA line joining points that are in antiphase
- DA line parallel to the direction of wave travel
2.In a reflection ray diagram, the angle of incidence is the angle between:
Easy
- Athe incident ray and the boundary surface
- Bthe incident ray and the normal
- Cthe incident ray and the reflected ray
- Dthe reflected ray and the boundary surface
3.A ray of light refracts as it passes from one medium into another. Which property of the light wave remains the same?
Easy
- AFrequency
- BWavelength
- CWave speed
- DAmplitude
4.Light from a monochromatic laser beam is incident on the surface of a body of water. What changes to the speed, wavelength, and frequency of the light wave would be observed as it passes from the air to the water?
Easy
- ASpeed decreases, wavelength decreases, frequency no change
- BSpeed no change, wavelength increases, frequency decreases
- CSpeed increases, wavelength decreases, frequency no change
- DSpeed decreases, wavelength no change, frequency increases
5.Which row correctly describes the conditions for constructive and destructive interference in a double-slit diffraction pattern?
Medium
- AConstructive: crest + crest; Destructive: trough + trough
- BConstructive: crest + trough; Destructive: trough + trough
- CConstructive: trough + trough; Destructive: crest + crest
- DConstructive: crest + crest; Destructive: crest + trough
6.For fringes to be observed in a double-slit interference experiment, the light emitted from each slit must be:
Easy
- Amonochromatic
- Bin phase
- Cof equal intensity
- Dcoherent
7.Which of the following processes changes the frequency of a wave?
Easy
- AReflection
- BRefraction
- CDiffraction
- DNone of the above
8.What is the purpose of the single slit in a Young's double-slit experiment?
Medium
- ATo make sure there is equal intensity in the double-slits
- BTo make sure the light is coherent upon the double-slits
- CTo decrease intensity for the double-slits
- DTo reduce the wavelength of the light

Plus de questions

9.Which of the following changes would increase the distance between adjacent fringes in a double-slit interference pattern?
Medium
- ADecrease the width of all the slits
- BMove the screen closer to the slits
- CUse light of a higher frequency
- DDecrease the distance between the two slits
10.Two point sources, S1 and S2, emit identical sound waves of intensity I0. The waves leaving S1 and S2 are in phase and arrive at point X. The wavelength of the sound is 3.0 m. Point X is 18.0 m from S1 and 10.5 m from S2. What intensity of sound would be heard by a person standing at point X?
Medium
- AZero
- BI0/4
- C2I0
- D4I0
11.Waves emitted from sources V and W are initially in phase and have equal wavelengths. Point A is not equidistant between V and W. The waves interfere destructively at point A, where the path difference is 0.30 m. What is the maximum possible value of the wavelength of the waves?
Medium
- A0.12 m
- B0.20 m
- C0.30 m
- D0.60 m
12.The diagram shows an arrangement for a two-slit interference experiment. Coherent light of frequency f is incident on two narrow parallel slits S1 and S2. An interference pattern is observed on a screen a distance away. The central bright fringe is observed at point O, and the next bright fringe is observed at point P. The speed of light is c. The distance S1P – S2P is equal to:
Medium
- Ac/f
- Bc/(2f)
- Cf/c
- Df/(2c)
13.A flat plate made of glass has a refractive index of n = 1.52. What is the speed of light within this material?
Medium
- A1.36 × 10⁸ m s^-1
- B1.67 × 10⁸ m s^-1
- C1.97 × 10⁸ m s^-1
- D2.66 × 10⁸ m s^-1
14.A light ray is incident on an air–diamond boundary. The refractive index of diamond is greater than 1. What changes to the speed, frequency, and wavelength of the light wave would be observed as it passes from the air to the diamond?
Medium
- ASpeed decreases, frequency stays constant, wavelength decreases
- BSpeed increases, frequency decreases, wavelength stays constant
- CSpeed stays constant, frequency decreases, wavelength increases
- DSpeed increases, frequency stays constant, wavelength increases
15.Diffraction can be observed in:
Easy
- Aall waves
- Bsound waves only
- Ctransverse waves only
- Dlight waves only
16.Two waves from individual point sources meet at a point. For interference to be observed at the point, the waves must:
Easy
- Ahave equal amplitudes
- Bhave equal wavelengths
- Chave a constant phase difference
- Dbe electromagnetic
17.Which of the following statements about wavefronts are correct? (select all that apply)
Medium
- AWavefronts are lines joining all points that oscillate in phase.
- BWavefronts are perpendicular to the direction of energy transfer.
- CThe distance between successive peak wavefronts is equal to the wavelength.
- DWavefronts are always straight lines.
- ECircular wavefronts are three-dimensional.
18.Which of the following are conditions necessary for total internal reflection to occur? (select all that apply)
Medium
- AThe refractive index of the second medium must be less than the refractive index of the first.
- BThe angle of incidence must be greater than the critical angle.
- CThe angle of incidence must be less than the critical angle.
- DThe refractive index of the second medium must be greater than the refractive index of the first.
- EThe light must be monochromatic.
19.When a wave is reflected, its frequency, wavelength and speed do not change.
Easy
True or false?
20.When a wave travels from a less dense medium into a denser medium, it bends away from the normal.
Easy
True or false?
21.Diffraction is most noticeable when the wavelength of the wave is much smaller than the width of the gap.
Easy
True or false?
22.In a double-slit interference pattern, the bright fringes are formed by constructive interference and have equal maximum intensity.
Medium
True or false?
23.Match each wave behaviour to its correct description.
Medium
- Reflection
- Refraction
- Diffraction
- Superposition
- The spreading out of waves after passing through a narrow gap or around an obstruction
- The change in direction of a wave when it passes through a boundary between media of different densities
- The combination of displacements when two or more waves overlap at a point
- The bouncing back of a wave at a boundary between two media
24.Place the following steps in the correct order to describe how a wave refracts when passing from air into water at an angle.
Medium
- The wavefront hits the boundary and part of it slows down first.
- The wavefront changes direction, bending towards the normal.
- The wave continues into the water with a shorter wavelength.
- The incident ray approaches the boundary at an angle to the normal.
25.A surface wave on water spreads out from a point source. What shape are its wavefronts?
Easy
- ACircular
- BSpherical
- CStraight parallel lines
- DElliptical
26.Which of the following statements about wavefronts and rays are correct? (select all that apply)
Medium
- AA wavefront joins points that oscillate in phase
- BRays are perpendicular to wavefronts
- CThe distance between successive peak wavefronts equals the wavelength
- DRays are parallel to the wavefronts
- EWavefronts show the direction of energy transfer
27.Match each wave behaviour to the correct description.
Medium
- Reflection
- Refraction
- Transmission
- Absorption
- Wave bounces back into the original medium at a boundary
- Wave changes direction when it crosses a boundary between media of different densities
- Wave passes through a substance and appears on the opposite side of a boundary
- Wave energy is taken in by the material it enters
28.Water waves travel from deep water into shallow water. Which row correctly describes what happens to the speed and wavelength of the waves?
Medium
- ASpeed decreases, wavelength decreases
- BSpeed increases, wavelength increases
- CSpeed decreases, wavelength increases
- DSpeed stays the same, wavelength decreases
29.Diffraction is the spreading out of waves after they pass through a narrow gap or around an obstruction.
Easy
True or false?
30.A wave passes from air into glass. Which of the following properties of the wave change at the boundary? (select all that apply)
Medium
- ASpeed
- BWavelength
- CFrequency
- DDirection of travel
- EColour
31.Light travels from air into a medium of refractive index 1.5. The speed of light in air is 3.0 × 10⁸ m/s. What is the speed of light in the medium?
Medium
- A2.0 × 10⁸ m/s
- B4.5 × 10⁸ m/s
- C1.5 × 10⁸ m/s
- D3.0 × 10⁸ m/s
32.Two coherent waves meet at a point. Their path difference is 2.5λ. What type of interference occurs at this point?
Medium
- ADestructive interference
- BConstructive interference
- CNo interference
- DPartially constructive interference
33.In a Young's double-slit experiment, which of the following changes would increase the fringe spacing s on the screen? (select all that apply)
Hard
- AIncreasing the wavelength of the light
- BIncreasing the distance between the slits and the screen
- CDecreasing the separation between the two slits
- DIncreasing the separation between the two slits
- EUsing light of higher frequency
34.A wavefront diagram shows a series of parallel straight wavefronts. The distance between successive wavefronts is 0.20 m. A ray is drawn perpendicular to the wavefronts. What is the wavelength of the wave?
Medium
- A0.10 m
- B0.20 m
- C0.40 m
- DIt cannot be determined from the diagram
35.A student shines a laser at a glass block. The angle between the incident ray and the glass surface is 35°. What is the angle of incidence?
Medium
- A35°
- B55°
- C70°
- D90°
36.A ray of light travels from air into a transparent plastic block. The angle of incidence is 40° and the angle of refraction is 25°. What is the refractive index of the plastic?
Medium
- A0.65
- B1.52
- C1.00
- D2.00
37.Light of wavelength 600 nm in air enters a medium of refractive index 1.5. What is the wavelength of the light in the medium?
Hard
- A200 nm
- B400 nm
- C600 nm
- D900 nm
38.In a Young's double-slit experiment, the slit separation is 0.50 mm, the screen distance is 2.0 m, and the wavelength is 600 nm. What is the fringe spacing?
Medium
- A0.24 mm
- B1.2 mm
- C2.4 mm
- D4.8 mm
39.Water waves pass from deep water into shallow water. The wavefronts are shown. What happens to the speed and wavelength of the waves?
Medium
- ASpeed decreases, wavelength decreases
- BSpeed increases, wavelength increases
- CSpeed decreases, wavelength increases
- DSpeed stays the same, wavelength decreases
40.A sound wave of frequency 1700 Hz travels through air at 340 m/s and passes through a gap of width 0.20 m. Diffraction is most noticeable when the gap width is similar to the wavelength. What is the wavelength of the sound, and will diffraction be noticeable?
Medium
- A0.10 m, not noticeable
- B0.20 m, noticeable
- C0.40 m, noticeable
- D2.0 m, noticeable
41.Light travels from a material with refractive index 1.2 into air. Calculate the critical angle of the material, in degrees, to the nearest degree.
Medium
42.A wave has a frequency of 3400 Hz and travels at a speed of 340 m/s. Calculate its wavelength in metres.
Medium
43.Complete the sentence about coherence.
Easy
For waves to be coherent, they must have the same ____ and a constant ____ difference.
44.Complete the conditions for constructive and destructive interference.
Medium
The condition for constructive interference is path difference = ____λ, and for destructive interference is path difference = (n + ____ )λ.
45.What is the name of the angle between the incident ray and the normal called?
Easy
46.What term describes the difference in distance travelled by two waves from their sources to a point where they meet?
Medium
47.A light ray travels from glass (n = 1.50) into air (n = 1.00). Calculate the critical angle of the glass, in degrees, to 1 decimal place.
Medium
48.Complete the conditions for total internal reflection to occur.
Medium
The refractive index of the second medium must be ____ than the refractive index of the first medium, and the angle of incidence must be ____ than the critical angle.
49.A light ray travels from water (n = 1.33) into air (n = 1.00). Calculate the critical angle of the water–air boundary, in degrees, to 1 decimal place.
Medium
50.A laser emits light of frequency 5.0 × 10¹⁴ Hz. The light passes through a double slit with separation 0.25 mm, and the screen is 3.0 m away. Calculate the fringe spacing in millimetres, to 1 decimal place.
Medium
51.Complete the statement about the conditions for total internal reflection.
Medium
Total internal reflection occurs when light travels from a ____ medium to a ____ medium and the angle of incidence is greater than the ____ angle.
52.A wave passes from air into glass. Complete the sentence describing what happens to its properties.
Medium
When light enters glass from air, its speed ____, its wavelength ____, and its frequency ____.
53.Explain why a single slit is used in Young's double-slit experiment.
Hard
54.Explain the difference between constructive and destructive interference in terms of phase and amplitude.
Hard
55.Explain why total internal reflection can only occur when light travels from a denser medium into a less dense medium.
Hard
56.A student sets up a Young's double-slit experiment but observes no clear interference pattern. Suggest two reasons why this might happen and explain how each could be corrected.
Hard
57.A student shines a laser through a double slit and observes a pattern of bright and dark fringes on a screen. Explain how the bright and dark fringes are formed.
Hard
58.Light travels from a material with refractive index 1.2 into air. Calculate the critical angle of the material, in degrees, to the nearest degree.
Medium
- A68 °
- B50 °
- C56 °
- D62 °
59.A wave has a frequency of 3400 Hz and travels at a speed of 340 m/s. Calculate its wavelength in metres.
Medium
- A-0.9 m
- B2.1 m
- C0.1 m
- D1.1 m
60.A light ray travels from glass (n = 1.50) into air (n = 1.00). Calculate the critical angle of the glass, in degrees, to 1 decimal place.
Medium
- A37.6°
- B50.2°
- C46°
- D41.8°
61.A light ray travels from water (n = 1.33) into air (n = 1.00). Calculate the critical angle of the water–air boundary, in degrees, to 1 decimal place.
Medium
- A53.7°
- B48.8°
- C43.9°
- D58.6°
62.A laser emits light of frequency 5.0 × 10¹⁴ Hz. The light passes through a double slit with separation 0.25 mm, and the screen is 3.0 m away. Calculate the fringe spacing in millimetres, to 1 decimal place.
Medium
- A8.2 mm
- B7.2 mm
- C9.2 mm
- D6.2 mm

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