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WorksheetsP.3.3.2 Refraction, diffraction, and interference
Total questions: 55
Worksheet time: 28mins
In the diagram, P is the source of a wave of frequency 50 Hz
The wave travels to R by two routes, P → Q → R and P → R. The speed of the wave is 30 m s−1
What is the path difference between the two waves at R in terms of the wavelength λ of the waves?
4.8λ
8.0λ
13.3λ
20.0λ
Light from a point source passes through a single slit and is then incident on a double-slit arrangement. An interference pattern is observed on the screen.
What will increase the fringe spacing?
increasing the separation of the single slit and the double slit
increasing the width of the single slit
decreasing the distance between the double slits and the screen
decreasing the separation of the double slits
When a monochromatic light source is incident on two slits of the same width an interference pattern is produced.
One slit is then covered with opaque black paper.
What is the effect of covering one slit on the resulting interference pattern?
The intensity of the central maximum will increase
The width of the central maximum decreases
Fewer maxima are observed
The outer maxima become wider
Two loudspeakers emit sound waves.
Which of the following gives the correct frequency condition and the correct phase condition for the waves from the loudspeakers to be coherent?
Frequency condition: same frequency
Phase condition: variable phase difference
Frequency condition: constant frequency difference
Phase condition: constant phase difference
Frequency condition: constant frequency difference
Phase condition: in phase
Frequency condition: same frequency
Phase condition: constant phase difference
When a parallel beam of monochromatic light is directed at two narrow slits, S1 and S2, interference fringes are observed on a screen.
Which of the following gives the changes that will increase the spacing of the fringes?
Slit spacing: halved
Distance from slits to screen: halved
Slit spacing: halved
Distance from slits to screen: doubled
Slit spacing: doubled
Distance from slits to screen: halved
Slit spacing: doubled
Distance from slits to screen: doubled
Two coherent sources generate sound waves of wavelength 0.40 m. The waves leave the sources in phase. A detector some distance from the sources receives the sound waves. The path difference between the detector and the sources is 0.90 m.
What is the phase difference between the waves arriving at the detector?
zero
45°
90°
180°
Monochromatic light of wavelength 600 nm is used to illuminate a pair of slits 0.50 mm apart. The fringes are observed at a distance of 1.50 m from the slits.
What is the separation of the fringes?
2.0 × 10−7 mm
1.8 × 10−3 mm
5.6 × 10−1 mm
1.8 mm
A light source emits light which is a mixture of two wavelength, λ1 and λ2. When the light is incident on a diffraction grating it is found that the fifth order of light of wavelength λ1 occurs at the same angle as the fourth order for light of wavelength λ2. If λ1 is 480 nm what is λ2?
400 nm
480 nm
600 nm
750 nm
When comparing X-rays with UV radiation, which statement is correct?
X-rays have a lower frequency.
X-rays travel faster in a vacuum.
X-rays do not show diffraction and interference effects.
Using the same element, photoelectrons emitted using X-rays have the greater maximum kinetic energy.
Monochromatic light of wavelength 490 nm falls normally on a diffraction grating that has 6 × 105 lines per metre. Which one of the following is correct?
The first order is observed at angle of diffraction of 17°.
The second order is observed at angle of diffraction of 34°.
The third and higher orders are not produced.
A grating with more lines per metre could produce more orders.
Interference maxima produced by a double source are observed at a distance of 1.0 m from the sources. In which one of the following cases are the maxima closest together?
red light of wavelength 700 nm from sources 4.0 mm apart
sound waves of wavelength 20 mm from sources 50 mm apart
blue light of wavelength 450 nm from sources 2.0 mm apart
surface water waves of wavelength 10 mm from sources 200 mm apart
The diagram shows a microwave transmitter T which directs microwaves of wavelength eat two slits S1 and S2 formed by metal plates. The microwaves that pass through the two slits are detected by a receiver.
When the receiver is moved to P from O, which is equidistant from S1 and S2, the signal received decreases from a maximum to a minimum. Which one of the following statements is a correct deduction from this observation?
The path difference S1O – S2O = 0.5 λ
The path difference S1O – S2O = λ
The path difference S1P – S2P = 0.5 λ
The path difference S1P – S2P = λ
Point sources of sound of the same frequency are placed at S1 and S2. When a sound detector is slowly moved along the line PQ, consecutive maxima of sound intensity are detected at W and Y and consecutive minima at X and Z. Which one of the following is a correct expression for the wavelength of the sound?
S1X – S1W
S1Y – S1X
S1X – S2X
S1Y – S2Y
In a Young’s double slit interference experiment, monochromatic light placed behind a single slit illuminates two narrow slits and the interference pattern is observed on a screen placed some distance away from the slits. Which one of the following decreases the separation of the fringes?
increasing the width of the single slit
decreasing the separation of the double slits
increasing the distance between the double slits and the screen
using monochromatic light of higher frequency
Interference fringes, produced by monochromatic light, are viewed on a screen placed a distance D from a double slit system with slit separation s. The distance between the centres of two adjacent fringes (the fringe separation) is w. If both s and D are doubled, what will be the new fringe separation?
w/4
w
2w
4w
Coherent monochromatic light of wavelength λ emerges from the slits X and Y to form dark fringes at P, Q, R and S in a double slit apparatus. Which one of the following statements is true?
When the distance D is increased, the separation of the fringes increases.
When the distance between X and Y is increased, the separation of the fringes increases.
When the width of the slit T is decreased, the separation of the fringes decreases.
There is a dark fringe at P because (YP − XP) is 2λ .
In a double slit interference arrangement the fringe spacing is w when the wavelength of the radiation is λ, the distance between the double slits is s and the distance between the slits and the plane of the observed fringes is D. In which one of the following cases would the fringe spacing also be w?
A
B
C
D
A double slit interference experiment is performed using monochromatic light of wavelength λ. The centre of the observed pattern is a bright fringe. What is the path difference between two waves which interfere to give the third dark fringe from the centre?
0.5 λ
1.5 λ
2.5 λ
3.5 λ
In a Young’s double slits interference arrangement the fringe separation is s when the wavelength of the radiation is λ, the slit separation w and the distance between the slits and the plane of the observed fringes D. In which one of the following cases would the fringe separation also be s?
A
B
C
D
Young’s two slit interference pattern with red light of wavelength 7.0 × 10–7 m gives a fringe separation of 2.0 mm.
What separation, in mm, would be observed at the same place using blue light of wavelength 45 × 10–7 m?
0.65
1.3
2.6
3.1
The diagram represents the experimental arrangement used to produce interference fringes in Young’s double slit experiment.
The spacing of the fringes on the screen will increase if
the width of the single slit is increased
the distance XY between the two slits is increased
a light source of lower frequency is used
the distance between the single and double slits is decreased
A diffraction grating is illuminated normally with light of wavelength 6.5 × 10–7 m. When a screen is 1.5 m from the grating, the distance between the zero and first-order maxima on the screen is 0.30 m.
What is the number of lines per mm of the diffraction grating?
3.3 × 10–6
3.3 × 10–3
3.0 × 102
3.0 × 105
A diffraction grating has 500 lines per mm. When monochromatic light is incident normally on the grating the third-order spectral line is formed at an angle of 60° from the normal to the grating.
What is the wavelength of the monochromatic light?
220 nm
580 nm
960 nm
1700 nm
Which statement suggests that electrons have wave properties?
Electrons are emitted in photoelectric effect experiments.
Electrons are released when atoms are ionised.
Electrons produce dark rings in diffraction experiments.
Electron transitions in atoms produce line spectra.
Intensity maxima are produced on a screen when a parallel beam of monochromatic light is incident on a diffraction grating. Light of a longer wavelength can be used or the distance from the diffraction grating to the screen can be increased.
Which row gives the change in appearance of the maxima when these changes are made independently?
Longer wavelength: closer together
Distance from grating to screen increased: more widely spaced
Longer wavelength: more widely spaced
Distance from grating to screen increased: more widely spaced
Longer wavelength: more widely spaced
Distance from grating to screen increased: closer together
Longer wavelength: closer together
Distance from grating to screen increased: closer together
Light of wavelength 500 nm is passed through a diffraction grating which has 400 lines per mm.
What is the angular separation between the two second-order maxima?
11.5°
23.1°
23.6°
47.2°
When a monochromatic light source is incident on two slits of the same width an interference pattern is produced.
One slit is then covered with opaque black paper.
What is the effect of covering one slit on the resulting interference pattern?
The intensity of the central maximum will increase
The width of the central maximum decreases
Fewer maxima are observed
The outer maxima become wider
When light of wavelength 5.0 × 10–7 m is incident normally on a diffraction grating the fourth-order maximum is observed at an angle of 30°.
What is the number of lines per mm on the diffraction grating?
2.5 × 102
2.5 × 105
1.0 × 103
1.0 × 106
Which of the following statements about the behaviour of waves is incorrect?
All waves can be diffracted.
All waves can be made to undergo superposition.
All waves can be refracted.
All waves can be polarised.
A parallel beam of monochromatic light is directed normally at a plane transmission grating which has N slits per metre. The second order diffracted beam is at angle θ to the zero order transmitted beam.
The grating is then replaced by a plane transmission grating which has 2N slits per metre. Which one of the following statements is correct?
With the first grating, the first order beam is at angle 0.5θ to the zero order transmitted beam.
With the second grating, the first order beam is at angle 0.5θ to the zero order transmitted beam.
With the second grating, the first order beam is at angle θ to the zero order transmitted beam.
With the second grating, the second order beam is at angle θ to the zero order transmitted beam.
Microwaves from a transmitter are incident on a gap between two metal plates. The microwaves that pass through the gap are detected by a receiver.
The receiver is placed at O.
What change causes the received signal to decrease and then increase?
make the gap narrower
move the receiver towards X
rotate the receiver through 90°
move the transmitter away from the receiver
Electrons and protons in two beams are travelling at the same speed. The beams are diffracted by objects of the same size.
Which correctly compares the de Broglie wavelength λe of the electrons with the de Broglie wavelength λp of the protons and the width of the diffraction patterns that are produced by these beams?
A
B
C
D
A diffraction pattern is formed by passing monochromatic light through a single slit. If the width of the single slit is reduced, which of the following is true?
Width of central maximum: unchanged
Intensity of central maximum: decreases
Width of central maximum: increases
Intensity of central maximum: increases
Width of central maximum: increases
Intensity of central maximum: decreases
Width of central maximum: decreases
Intensity of central maximum: decreases
When comparing X-rays with UV radiation, which statement is correct?
X-rays have a lower frequency.
X-rays travel faster in a vacuum.
X-rays do not show diffraction and interference effects.
Using the same element, photoelectrons emitted using X-rays have the greater maximum kinetic energy.
In a diffraction-grating experiment the maxima are produced on a screen. What causes the separation of the maxima of the diffraction pattern to decrease?
using light with a longer wavelength
increasing the distance between the screen and grating
increasing the distance between the source and grating
using a grating with a greater slit separation
White light passes through a single narrow slit and illuminates a screen. What is observed on the screen?
a set of equally spaced white fringes
a central maximum made up of a spectrum surrounded by white fringes
a white central maximum surrounded by coloured fringes
a single narrow white line
In a double slit system used to produce interference fringes, the separation of the slits is s and the width of each slit is x. L is a source of monochromatic light. Which one of the following changes would decrease the separation of the fringes seen on the screen?
moving the screen closer to the double slits
decreasing the width, x, of each slit, but keeping s constant
decreasing the separation, s, of the slits
exchanging L for a monochromatic source of longer wavelength
The diagram above shows the first four diffraction orders each side of the zero order when a beam of monochromatic light is incident normally on a diffraction grating of slit separation d. All the angles of diffraction are small. Which one of the patterns, drawn on the same scale, is obtained when the grating is exchanged for one with a slit separation d/2 ?
Light of wavelength λ is incident normally on a diffraction grating for which adjacent lines are a distance 3λ apart. What is the angle between the second order maximum and the straight-through position?
9.6°
20°
42°
There is no second order maximum.
Light of wavelength λ is incident normally on a diffraction grating of slit separation 4λ. What is the angle between the second order maximum and third order maximum?
14.5°
18.6°
48.6°
71.4°
A narrow beam of monochromatic light falls on a diffraction grating at normal incidence. The second order diffracted beam makes an angle of 45° with the grating. What is the highest order visible with this grating at this wavelength?
2
3
4
5
Monochromatic light of wavelength 590 nm is incident normally on a plane diffraction grating having 4 × 10 5 lines m−1 . An interference pattern is produced. What is the highest order visible in this interference pattern?
2
3
4
5
Using a diffraction grating with monochromatic light of wavelength 500 nm incident normally, a student found the 2nd order diffracted maxima in a direction at 30° to the central bright fringe. What is the number of lines per metre on the grating?
2 × 104
2 × 105
4 × 105
5 × 105
A ray of light is incident on a glass–air boundary of a rectangular block as shown.
The refractive index of this glass is 1.5
The refractive index of air is 1.0
The angle of incidence of the light at the first glass–air boundary is 44°
What is the path of the ray of light?
A
B
C
D
Rays of light are incident at the same angle θ on the core–cladding boundary of optical fibres P and Q. The cores of P and Q have the same refractive index n.
P and Q are the same length L. The core diameter of P is half that of Q.
The time for the ray to travel along optical fibre P is (nL)/(csinθ) where c is the speed of light in a vacuum.
What is the time for the ray to travel along optical fibre Q?
An electromagnetic wave enters a fibre-optic cable from air. On entering the cable, the wave slows down to three-fifths of its original speed.
What is the refractive index of the core of the fibre-optic cable?
0.67
1.33
1.50
1.67
The diagram shows part of the path of a ray of light through a right-angled prism.
The prism is made of glass of refractive index 1.5.
The incident light ray is parallel to the face XY. The ray is refracted towards the face XY.
What is the path of the ray after it is incident on face XY?
Which row shows the change in velocity, frequency and wavelength of an electromagnetic wave as it travels from an optically less dense to an optically more dense medium?
A
B
C
D
The diagram shows a ray of light travelling in air and incident on a glass block of refractive index 1.5.
What is the angle of refraction in the glass?
22.5°
23.3°
33.1°
59.4°
A layer of liquid of refractive index 1.6 covers the horizontal flat surface of a glass block of refractive index 1.5. A ray of light strikes the boundary between them at an angle such that it travels along the boundary afterwards.
How does the ray strike the boundary?
it travels in glass at an angle of 70° to the boundary
it travels in glass at an angle of 20° to the boundary
it travels in the liquid at an angle of 70° to the boundary
it travels in the liquid at an angle of 20° to the boundary
Monochromatic light may be characterised by its speed, frequency and wavelength. Which of the following quantities change when monochromatic light passes from air into glass?
Speed only.
Speed and wavelength only.
Speed and frequency only.
Wavelength and frequency only.
Which of the following is correct when total internal reflection occurs?
the angle of incidence is less than the critical angle
the light meets an optically less dense medium
the light enters a medium with a higher refractive index
the angles that the incident and refracted rays make with the normal are the same
What is the speed of light in glass of refractive index 1.42?
4.26 × 107 m s−1
2.11 × 108 m s−1
3.00 × 108 m s−1
4.73 × 108 m s−1
Figures 1 and 2 each show a ray of light incident on a water-air boundary. A, B, C and D show ray directions at the interface. Which of the following corresponds to a direction in which a ray cannot occur.
A
B
C
D
Figures 1 and 2 each show a ray of light incident on a water-air boundary. A, B, C and D show ray directions at the interface. Which of the following corresponds to the direction of the faintest ray.
A
B
C
D
