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 wave motion.
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 (e.g., water waves).
A spherical wave propagates in three dimensions and has spherical wavefronts (e.g., sound or light).
The distance between successive peak wavefronts (or trough wavefronts) is equal to the wavelength.
In diagrams, peaks are often represented with a darker line and troughs with a fainter line.

Reflection, Refraction & Transmission

When waves meet a boundary, they can be reflected, refracted, transmitted, or absorbed.
Reflection: a wave bounces back into the original medium; the angle of incidence equals the angle of reflection.
During reflection, the frequency, wavelength, and speed of the wave do not change.
Refraction is the change in direction of a wave when it passes between media of different densities, caused by a change in speed.
When a wave refracts, its speed and wavelength change, but its frequency remains the same.
Going from less dense to more dense: waves slow down, wavelength shortens, and the ray bends towards the normal.
Going from more dense to less dense: waves speed up, wavelength lengthens, and the ray bends away from the normal.
Transmission is the general term for a wave passing through a substance; refraction is a type of transmission.

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 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 larger, there is little diffraction.
When waves diffract through an aperture, their amplitude decreases because the barrier absorbs some wave energy.
Diffraction also occurs around a barrier: longer wavelengths diffract more, producing a smaller 'shadow' region behind the barrier.
When a barrier is 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 is a dimensionless quantity (no units); for air, n ≈ 1.
Snell's law relates the angles of incidence and refraction: n₁ sin θ₁ = n₂ sin θ₂, or n₁/n₂ = sin θ₂ / sin θ₁ = v₂ / v₁.
The angles of incidence and refraction are measured from the normal, which is drawn at 90° to the boundary.
When light passes from a less dense to a more dense medium, the refracted ray bends towards the normal and the wavelength decreases.
When light is incident along the normal (90° to the boundary), it passes straight through without changing direction.

Refraction of light

$Refraction of light$

Critical Angle & Total Internal Reflection

As the angle of incidence increases, the angle of refraction also increases until it reaches 90°; this angle of incidence is the critical angle θc.
The critical angle is given by sin θc = n₂ / n₁, where n₁ is the refractive index of the denser medium and n₂ is that of the less dense medium.
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.
Total internal reflection follows the law of reflection: angle of incidence = angle of reflection.

Partial reflection/refraction compared with total internal reflection (angle of incidence > critical angle)

$Partial reflection/refraction compared with total internal reflection (angle of incidence > critical angle)$

Superposition of Waves

The principle of superposition states that when two or more waves overlap at a point, the resultant displacement is the sum of the individual displacements.
Individual wave displacements may be positive or negative and are combined algebraically.
Superposition can be analysed using displacement–position or displacement–time graphs.
When two pulses meet, their displacements combine to form a resultant displacement; after interacting, they continue as normal.
Interference is the effect observed due to the superposition of two or more waves.

Interference of Waves

Constructive interference occurs when waves meet in phase (peak-to-peak or trough-to-trough), resulting in a larger amplitude.
Destructive interference occurs when waves meet in antiphase (peak-to-trough), resulting in cancellation.
For sustained interference, waves must 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, ...).

Young’s Double-Slit Experiment

Young's double-slit experiment produces an interference pattern using a single wave source passing through a double slit.
Lasers are commonly used because the light must be coherent and monochromatic.
The pattern consists of bright fringes (maxima) from constructive interference and dark fringes (minima) from destructive interference.
Each bright fringe is identical and has the same width and intensity.
The fringe spacing s is given by s = λD / d, where λ is the wavelength, D is the distance from slits to screen, and d is the slit separation.
Fringe spacing increases if the wavelength increases, the screen distance increases, or the slit separation decreases.
The order n of a maximum gives its position away from the central maximum (n = 0 is the central maximum).

Single-Slit Diffraction

Single-slit diffraction produces a pattern of bright and dark fringes on a screen.
The central maximum is the brightest and widest fringe.
Making the slit narrower increases the width of the central maximum and the fringe spacing.
Using a longer wavelength (e.g., red light) produces wider fringes than a shorter wavelength (e.g., blue light).
Increasing the distance between the slit and the screen increases the width of the fringes.
A modulated interference pattern is observed when single-slit diffraction combines with double-slit interference.

Diffraction Gratings

A diffraction grating consists of many parallel slits, producing sharper and brighter maxima than a double slit.
The condition for constructive interference (maxima) is d sin θ = nλ, where d is the slit spacing, θ is the angle of diffraction, and n is the order.
White light passed through a diffraction grating produces a spectrum; violet appears closest to the centre and red furthest away.
The number of visible orders depends on the wavelength and the slit spacing.

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1.In a reflection ray diagram, the angle of incidence is the angle between
Easy
- Athe incident ray and the normal.
- Bthe incident ray and the boundary surface.
- Cthe incident ray and the reflected ray.
- Dthe reflected ray and the boundary surface.
2.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
3.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
4.Diffraction can be observed in
Easy
- Aall waves
- Bsound waves only
- Ctransverse waves only
- Dlight waves only
5.For fringes to be observed in a double-slit interference experiment, the light emitted from each slit must be
Easy
- Acoherent.
- Bmonochromatic.
- Cin phase.
- Dof equal intensity.
6.White light is passed through a diffraction grating. Which colour appears closest to the centre of the pattern when viewed on a screen?
Medium
- AViolet
- BBlue
- CRed
- DGreen
7.Light of different wavelengths is incident on a single slit. A diffraction pattern is observed on a screen a distance away. What is the relationship between the wavelength of the light and the width of the bright fringes on the diffraction pattern?
Medium
- ARed light produces a diffraction pattern with the widest fringes.
- BBlue light produces a diffraction pattern with the widest fringes.
- CAll wavelengths of light produce bright fringes of equal width.
- DChanging the width of the slit is the only variable that affects the width of the bright fringes.
8.Monochromatic light is incident on a narrow slit to produce a diffraction pattern of bright and dark fringes on a screen. The slit is then made narrower. What is the change to the pattern observed on the screen?
Medium
- AThe fringe spacing will become wider.
- BThe intensity of the central maximum will increase.
- CThe fringe spacing will become narrower.
- DThe width of the central maximum will decrease.

Thêm câu hỏi

9.Monochromatic light is incident on a single slit. An intensity pattern is observed on a screen. The distance between the slit and the screen is then increased. What is the change to the pattern observed on the screen?
Medium
- AThe width of the fringes will increase.
- BThe intensity of the fringes will decrease.
- CThe intensity of the fringes will increase.
- DThe width of the fringes will decrease.
10.A modulated interference pattern is observed when
Easy
- Athe pattern from single-slit diffraction combines with the pattern from double-slit interference.
- Bthe light passing through the two slits is coherent.
- Cthe distance to the screen is much larger than the slit separation.
- Dthe interference is observed from two ideal, infinitely narrow slits.
11.A flat plate made of glass has a refractive index of n = 1.52. What is the speed of light within this material?
Medium
- A1.97 × 10⁸ m s^-1
- B1.36 × 10⁸ m s^-1
- C1.67 × 10⁸ m s^-1
- D2.66 × 10⁸ m s^-1
12.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
13.Which statement defines diffraction?
Easy
- AThe spreading out of waves after they pass through a narrow gap or around an obstruction
- BThe bouncing back of waves from a boundary between two media
- CThe change in direction of a wave when it passes between media of different densities
- DThe combination of two waves to give a resultant displacement equal to the sum of the individual displacements
14.A wave passes through an aperture. Which condition makes the diffraction effect most noticeable?
Easy
- AThe wavelength of the wave is much smaller than the width of the aperture
- BThe wavelength of the wave is similar in size to the width of the aperture
- CThe wavelength of the wave is much larger than the amplitude of the wave
- DThe amplitude of the wave is much larger than the width of the aperture
15.Which of the following statements about reflection are correct? (select all that apply)
Medium
- AThe angle of incidence equals the angle of reflection
- BThe frequency of the wave does not change during reflection
- CThe speed of the wave changes during reflection
- DThe wavelength of the wave does not change during reflection
- EThe wave passes into the second medium
16.Which of the following statements about refraction are correct? (select all that apply)
Medium
- ARefraction is caused by a change in the speed of different parts of the wavefront as they hit the boundary
- BThe frequency of the wave changes when it refracts
- CWhen light passes from a less dense to a more dense medium it bends towards the normal
- DRefraction is a type of transmission
- EWhen light passes from a less dense to a more dense medium its wavelength increases
17.When a wave refracts at a boundary, its frequency remains the same.
Easy
True or false?
18.Total internal reflection can occur when light travels from a less dense medium into a more dense medium.
Medium
True or false?
19.Match each wave behaviour to its correct description.
Medium
- Reflection
- Refraction
- Transmission
- Diffraction
- A wave passes through a substance
- A wave spreads out after passing through a narrow gap or around an obstruction
- A wave bounces back into the original medium at a boundary
- The change in direction of a wave when it crosses a boundary between media of different densities
20.Match each quantity in the double-slit equation s = λD/d to its meaning.
Medium
- s
- λ
- D
- d
- Separation between the slits
- Separation between successive fringes on the screen
- Distance between the screen and the slits
- Wavelength of the incident light
21.Place the following stages of light passing through a Young's double-slit experiment into the correct order.
Medium
- Light passes through a single slit
- Light is diffracted to produce two coherent sources at the double slit
- Light from the two slits diffracts and overlaps
- Bright and dark fringes form on the screen
22.Which change would increase the separation between adjacent fringes?
Medium
- ADecrease the distance between the two slits
- BIncrease the distance between the two slits
- CUse light of a higher frequency
- DMove the screen closer to the slits
23.What is the path difference between the light from the two slits at a point on the screen where a dark fringe is formed?
Medium
- AAn odd number of half-wavelengths
- BA whole number of wavelengths
- CZero
- DAn even number of wavelengths
24.A wavefront diagram shows a wave with wavefronts spaced 0.5 m apart. What is the wavelength of the wave?
Medium
- A0.5 m
- B1.0 m
- C0.25 m
- D2.0 m
25.A ray of light travels from air into a medium with refractive index 1.5. If the angle of incidence is 30°, what is the angle of refraction?
Medium
- A19.5°
- B30°
- C48.6°
- D60°
26.Which of the following statements about diffraction are correct? (select all that apply)
Medium
- ADiffraction is the spreading out of waves after passing through a narrow gap or around an obstacle.
- BDiffraction is most noticeable when the wavelength is much smaller than the gap size.
- CDiffraction can occur for all types of waves, including sound and light.
- DThe amount of diffraction increases as the gap size decreases relative to the wavelength.
- EDiffraction only occurs for transverse waves.
27.When a wave is reflected from a boundary, its frequency remains unchanged.
Easy
True or false?
28.In a Young's double-slit experiment, the separation between adjacent bright fringes is 2.0 mm. If the distance between the slits and the screen is doubled while all else remains constant, what is the new fringe separation?
Medium
- A1.0 mm
- B2.0 mm
- C4.0 mm
- D8.0 mm
29.Match each wave behaviour with its correct description.
Medium
- Reflection
- Refraction
- Diffraction
- Superposition
- The spreading out of waves after passing through a narrow gap or around an obstacle
- The change in direction of a wave when it passes through a boundary between media of different densities
- The combination of amplitudes when two or more waves overlap at a point
- The bouncing back of a wave when it hits a boundary between two media
30.Place the following steps of light passing through a Young's double-slit experiment in the correct order.
Medium
- Light passes through a single slit and diffracts.
- The diffracted light illuminates two closely spaced slits.
- The light from the two slits interferes constructively and destructively.
- A pattern of bright and dark fringes is observed on a screen.
31.A diffraction grating with 500 lines per mm is illuminated with monochromatic light of wavelength 600 nm. At what angle does the first-order maximum occur?
Medium
- A8.6°
- B17.5°
- C30.0°
- D45.0°
32.In a Young's double-slit experiment, a laser of wavelength 630 nm is used with slits separated by 0.25 mm and a screen 3.0 m away. The fringe spacing measured is 7.2 mm. A student then replaces the laser with one of wavelength 420 nm, keeping all other apparatus unchanged. What is the new fringe spacing?
Medium
- A4.8 mm
- B10.8 mm
- C7.2 mm
- D2.4 mm
33.A student sets up a double-slit experiment and observes the fringe pattern on a screen. They then place the whole apparatus under water (refractive index 1.33) so that the light travels through water between the slits and the screen. Which statement describes the effect on the pattern?
Medium
- AThe fringe spacing decreases because the wavelength of the light in water is shorter.
- BThe fringe spacing increases because the speed of light in water is lower.
- CThe fringe spacing is unchanged because the frequency of the light is unchanged.
- DThe fringe spacing is unchanged because the slit separation is unchanged.
34.A diffraction grating has 300 lines per mm. Monochromatic light of wavelength 500 nm is incident normally on the grating. At what angle does the second-order maximum appear?
Medium
- A17.5°
- B8.6°
- C35.7°
- D30.0°
35.In a double-slit experiment, the intensity of the light passing through one slit is reduced so that the two slits no longer produce waves of equal amplitude. Which feature of the interference pattern changes?
Hard
- AThe minima no longer have zero intensity.
- BThe positions of the maxima move closer together.
- CThe wavelength of the light changes.
- DThe fringe spacing doubles.
36.A student uses a microwave source and two slits to demonstrate interference. The detector records a series of maxima and minima as it is moved along a line parallel to the slits. Which change would increase the distance between adjacent maxima?
Medium
- AIncreasing the wavelength of the microwaves.
- BDecreasing the distance from the slits to the detector.
- CIncreasing the separation of the two slits.
- DDecreasing the wavelength of the microwaves.
37.A parallel beam of light of wavelength 600 nm falls normally on a single slit of width 0.12 mm. A screen is placed 2.0 m away. What is the approximate width of the central maximum?
Medium
- A20 mm
- B10 mm
- C40 mm
- D5 mm
38.Light of wavelength 5.5 × 10⁻⁷ m is incident normally on a diffraction grating with 5000 lines per cm. What is the highest order maximum that can be observed?
Hard
- A3
- B2
- C4
- D5
39.In a Young's double-slit experiment, which of the following changes would increase the separation between adjacent bright fringes on the screen? (select all that apply)
Medium
- AUsing light of longer wavelength
- BMoving the screen further from the slits
- CDecreasing the separation of the slits
- DUsing light of higher frequency
- EIncreasing the width of each slit
40.A student is investigating total internal reflection using a semicircular glass block. Which of the following statements about their method are correct? (select all that apply)
Hard
- AThe angle of incidence must be measured from the normal to the flat surface.
- BThe light must travel from the glass into the air to observe total internal reflection.
- CThe critical angle can be found by increasing the angle of incidence until the refracted ray disappears.
- DTotal internal reflection can be observed when light travels from air into the glass block.
- EThe refracted ray becomes brighter than the reflected ray at the critical angle.
41.Light of wavelength 6.0 × 10⁻⁷ m passes through two slits separated by 0.30 mm. The screen is 2.0 m from the slits. Calculate the separation between adjacent fringes on the screen, in mm.
Medium
42.Light travels from a material of refractive index 1.2 into air. Calculate the critical angle of the material, in degrees, to the nearest degree.
Medium
43.Complete the sentence about wave behaviour at a boundary.
Easy
When a wave refracts, its speed and ____ change, but its ____ remains the same.
44.Complete the conditions for total internal reflection.
Medium
Total internal reflection requires that the refractive index of the second medium is ____ than that of the first, and that the angle of incidence is ____ than the critical angle.
45.What name is given to the angle of incidence at which the angle of refraction is exactly 90°?
Easy
46.What term describes two waves that have the same frequency and a constant phase difference?
Easy
47.A light ray travels from water (n = 1.33) into air. Calculate the critical angle for total internal reflection, in degrees, to the nearest degree.
Medium
48.Complete the sentence about total internal reflection.
Easy
Total internal reflection occurs when light travels from a medium of ____ refractive index to a medium of ____ refractive index, and the angle of incidence is greater than the ____ angle.
49.What term describes the difference in distance travelled by two waves from their sources to a point where they meet?
Medium
50.A light ray travels from air into a medium with refractive index 1.5. If the angle of incidence is 30°, calculate the angle of refraction, in degrees, to the nearest degree.
Medium
51.Light of wavelength 5.0 × 10⁻⁷ m is incident on a diffraction grating with 400 lines per mm. Calculate the angle of the first-order maximum, in degrees, to the nearest degree.
Medium
52.A wave has a frequency of 250 Hz and a wavelength of 1.2 m. Calculate its speed in m/s.
Medium
53.Explain why the light passing through the two slits in Young's double-slit experiment must be coherent and monochromatic.
Hard
54.Explain why the diffraction of sound waves through a doorway is more noticeable than the diffraction of light waves through the same doorway.
Hard
55.A student is asked to measure the wavelength of light using a diffraction grating. Describe how the student should set up the apparatus and take measurements to obtain an accurate value for the wavelength.
Hard
56.Explain why the central maximum in a single-slit diffraction pattern becomes wider when the slit width is decreased, and why the intensity of the central maximum decreases.
Hard
57.The student then replaces the grating with one having 800 lines per mm. State and explain what happens to the angle of the first-order maximum.
Hard
58.Light of wavelength 6.0 × 10⁻⁷ m passes through two slits separated by 0.30 mm. The screen is 2.0 m from the slits. Calculate the separation between adjacent fringes on the screen, in mm.
Medium
- A4 mm
- B5 mm
- C6 mm
- D3 mm
59.Light travels from a material of refractive index 1.2 into air. Calculate the critical angle of the material, in degrees, to the nearest degree.
Medium
- A50 °
- B68 °
- C56 °
- D62 °
60.A light ray travels from water (n = 1.33) into air. Calculate the critical angle for total internal reflection, in degrees, to the nearest degree.
Medium
- A44 °
- B59 °
- C49 °
- D54 °
61.A light ray travels from air into a medium with refractive index 1.5. If the angle of incidence is 30°, calculate the angle of refraction, in degrees, to the nearest degree.
Medium
- A20 °
- B21 °
- C18 °
- D19 °
62.Light of wavelength 5.0 × 10⁻⁷ m is incident on a diffraction grating with 400 lines per mm. Calculate the angle of the first-order maximum, in degrees, to the nearest degree.
Medium
- A13 °
- B14 °
- C12 °
- D11 °
63.A wave has a frequency of 250 Hz and a wavelength of 1.2 m. Calculate its speed in m/s.
Medium
- A270 m/s
- B330 m/s
- C300 m/s
- D360 m/s

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