Assignment 5: Waves and the particle nature of light

Introduction

Aims

In this assignment you will answer questions based on the contents of Section 4 of the course. You will:

? answer multiple choice questions

? describe practical situations and interpret measurements

? solve problems in materials and vibrations, using the methods taught in the Section, using the equations on the data sheet.

These are question types that are used in the 'A' level examination papers.

Links to the assessment requirements

The assessment objectives for the A level are to:

? demonstrate knowledge and understanding of scientific ideas, processes, techniques and procedures

? apply knowledge and understanding of scientific ideas, processes, techniques and procedures:

• in a theoretical context

• in a practical context

• when handling qualitative data

• when handling quantitative data

? analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to:

• make judgements and reach conclusions

• develop and refine practical design and procedures.

How your tutor will mark your work

Your tutor will assess the following aspects of your work:

? your application of appropriate physical principles

? your use of appropriate equations

? the accuracy of your calculations ? your use of appropriate units.

An error in calculation in one step of a question will not normally lead to a loss of marks in subsequent calculations, provided the principles are applied correctly and your answers are consistent with the figures you have used.

Are you ready to do this assignment?

Before you tackle this assignment, ensure that you have done the quizzes and most of the practice exam questions in each of Chapters 15 to 17 inclusive. This assignment also contains material from Core Practicals 6 and 8, with sample data for those who were not able to do the experiments.

In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler, graph paper and a calculator.

The Assignment

In calculations, use g = 9.81 m s-2 for the acceleration of free-fall unless told otherwise.

1 The frequency of vibration of a string may be decreased by

A Reducing its length

B Increasing the tension

C Increasing the mass per unit length of the string

D Decreasing the mass per unit length of the string

(1 mark)

2 A 100 W bulb emits 5% of its power as light. What is the visible light intensity at 1 m?

A 0.40 W m-2

B 1.2 W m-2

C 7.9 W m-2

D 1.6 W m-2

(1 mark)

3 Which three of the following statements are true in relation to coherent sources?

a) They have the same wavelength

b) They have the same amplitude

c) They have the same frequency

d) They have a constant phase relationship

Use the following key for your answer (1 mark)

Table 1 Key for question 3

Choice for your answer Factors from the list that are correct

A a), b) and c)

B a), c) and d)

C b), c) and d)

D a), b) and d)

4 Three of the following statements concerning standing and travelling waves are true. Which is the one that is not?

A The oscillations are all in phase between the nodes of a standing wave, but the phase varies continuously along the travelling wave

B Standing waves store energy but travelling waves transfer energy from one place to another

C Both standing waves and travelling waves store energy

D The amplitude of travelling waves is constant along the wave, but the amplitude of a standing wave varies from zero at a node to a maximum at an antinode.

(1 mark)

5 In the diffraction pattern produced by a single slit, the width of the central maximum can be made smaller by:

A Reducing the width of the slit

B Increasing the width of the slit

C Increasing the wavelength of the light

D Increasing the distance between the slit and the screen

(1 mark)

6 A red laser has a wavelength of 650 nm. What is the energy of the photons that it emits?

A 0.53 eV

B 1.9 x 10-19 J

C 8.5 x 10-20 J

D 1.9 eV

(1 mark)

7 A stringed instrument has a string that is 40 cm long. What is the wavelength of the fundamental mode when it is plucked?

A 40 cm

B 80 cm

C 160 cm

D 20 cm

(1 mark)

8 In Core Practical 6, the experiment to measure the speed of sound in air using a two channel oscilloscope, signal generator, microphone and loudspeaker, the following results were obtained for a signal of frequency 3 kHz:

Table 2 Data from the speed of sound experiment

Successive distances from the loudspeaker where the waves are in antiphase /cm

134.3 122.9 111.2 100.1 88.9 78.0 66.3 55.0

a) Use these data to calculate the mean wavelength of the sound, giving the uncertainty in this figure (3 marks)

b) Using the frequency given, calculate the speed of sound in air

(2 marks)

9 This question concerns the images formed by lenses.

a) Make a scale drawing to show how an image is formed by a diverging lens. The lens has a focal length of 10 cm, and the object is 5 cm from the centre of the lens. The object is 2 cm tall. Hint: the ray diagram will be much easier to draw if you use

squared paper. (4 marks)

b) Is the image real or virtual? Give a reason for your answer

(2 marks)

c) Use the lens formula, with the sign convention ‘real is positive’ and the given object distance and focal length to confirm that this image is in the correct place (2 marks)

d) Calculate the magnification, and compare it to the magnification measured from your drawing (2 marks) e) What is the power of this lens? (2 marks)

f) If you add a second lens to this, with a power of + 10 dioptres, what is the total power? (2 marks)

10 This question concerns refractive indices

The drawing (not to scale) shows a ray of light passing from water, through silica glass and into air.

a) Calculate the critical angle at the glass/air interface (2 marks)

b) Calculate the angle ?1 at the water/glass interface that will lead to the ray striking the glass/air interface at the critical angle

(4 marks)

11 The CD that was used in Assignment 1 was used to measure the wavelength of a green laser pointer. The spacing of the lines on the CD was 1.5 x 10-6 m.

The CD was placed 40 cm from a wall, and the distances from the central maximum of the green laser to the diffracted beam were measured to be:

Table 3 Measurements for Question 11

Distance from central maximum to the diffracted beam/ cm

15.5 15.5 15.2 15.6 15.7

Calculate the wavelength of the green laser (3 marks)

12 This question concerns polarisation.

a) Explain what is meant by polarisation of a wave. This should include a mention of which types of wave can, and which cannot,

be polarised (3 marks)

b) Explain why the two sheets of Polaroid pictured in the photographs below will both allow light through in one orientation, but when one is rotated by 90o light is no longer

transmitted. (4 marks)

Figure 2 Polaroid sheets oriented in the same way, and at right angles to one another

13 The bright light emitted by sodium lamps comes from a transition between electrons at an energy level of – 3.04 eV falling to an

energy level of -5.14 eV. Calculate the wavelength of the light emitted (2 marks) 14 A scanning electron microscope is operating with 25 keV electrons.

a) Calculate the energy, in J, possessed by the electrons (2 marks)

b) Calculate the velocity of the electron, given that the mass of an electron is 9.11 × 10-31 kg (2 marks) c) Calculate the momentum of the electrons (2 marks)

d) Hence calculate the wavelength of the electrons (2 marks)

e) What effect would increasing the electron energy have on the

wavelength, and what consequence would that have on the

resolution of the images? (2 marks)

In ultrasound, increasing the frequency improves the resolution of the image but,

f) what happens to the depth of the scan that you can obtain when the frequency is increased? (1 mark)

15 This question concerns the particulate nature of light.

a) Describe one experiment or observation that shows that light has wave properties and one experiment or observation that shows that it behaves as a stream of particles. Ensure that you explain precisely how each experiment leads to that conclusion.

(4 marks)

b) Green light of wavelength 550 nm is shone on potassium, which has a work function of 2.0 eV. Calculate the maximum kinetic energy of the photoelectrons emitted. (2 marks)

Total for the assignment 62 marks

Submit your assignment

When you have completed your assignment, submit it to your tutor for marking. Please convert your work into pdf format. Your tutor will send you helpful feedback and advice to help you progress through the course.

Introduction

Aims

In this assignment you will answer questions based on the contents of Section 4 of the course. You will:

? answer multiple choice questions

? describe practical situations and interpret measurements

? solve problems in materials and vibrations, using the methods taught in the Section, using the equations on the data sheet.

These are question types that are used in the 'A' level examination papers.

Links to the assessment requirements

The assessment objectives for the A level are to:

? demonstrate knowledge and understanding of scientific ideas, processes, techniques and procedures

? apply knowledge and understanding of scientific ideas, processes, techniques and procedures:

• in a theoretical context

• in a practical context

• when handling qualitative data

• when handling quantitative data

? analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to:

• make judgements and reach conclusions

• develop and refine practical design and procedures.

How your tutor will mark your work

Your tutor will assess the following aspects of your work:

? your application of appropriate physical principles

? your use of appropriate equations

? the accuracy of your calculations ? your use of appropriate units.

An error in calculation in one step of a question will not normally lead to a loss of marks in subsequent calculations, provided the principles are applied correctly and your answers are consistent with the figures you have used.

Are you ready to do this assignment?

Before you tackle this assignment, ensure that you have done the quizzes and most of the practice exam questions in each of Chapters 15 to 17 inclusive. This assignment also contains material from Core Practicals 6 and 8, with sample data for those who were not able to do the experiments.

In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler, graph paper and a calculator.

The Assignment

In calculations, use g = 9.81 m s-2 for the acceleration of free-fall unless told otherwise.

1 The frequency of vibration of a string may be decreased by

A Reducing its length

B Increasing the tension

C Increasing the mass per unit length of the string

D Decreasing the mass per unit length of the string

(1 mark)

2 A 100 W bulb emits 5% of its power as light. What is the visible light intensity at 1 m?

A 0.40 W m-2

B 1.2 W m-2

C 7.9 W m-2

D 1.6 W m-2

(1 mark)

3 Which three of the following statements are true in relation to coherent sources?

a) They have the same wavelength

b) They have the same amplitude

c) They have the same frequency

d) They have a constant phase relationship

Use the following key for your answer (1 mark)

Table 1 Key for question 3

Choice for your answer Factors from the list that are correct

A a), b) and c)

B a), c) and d)

C b), c) and d)

D a), b) and d)

4 Three of the following statements concerning standing and travelling waves are true. Which is the one that is not?

A The oscillations are all in phase between the nodes of a standing wave, but the phase varies continuously along the travelling wave

B Standing waves store energy but travelling waves transfer energy from one place to another

C Both standing waves and travelling waves store energy

D The amplitude of travelling waves is constant along the wave, but the amplitude of a standing wave varies from zero at a node to a maximum at an antinode.

(1 mark)

5 In the diffraction pattern produced by a single slit, the width of the central maximum can be made smaller by:

A Reducing the width of the slit

B Increasing the width of the slit

C Increasing the wavelength of the light

D Increasing the distance between the slit and the screen

(1 mark)

6 A red laser has a wavelength of 650 nm. What is the energy of the photons that it emits?

A 0.53 eV

B 1.9 x 10-19 J

C 8.5 x 10-20 J

D 1.9 eV

(1 mark)

7 A stringed instrument has a string that is 40 cm long. What is the wavelength of the fundamental mode when it is plucked?

A 40 cm

B 80 cm

C 160 cm

D 20 cm

(1 mark)

8 In Core Practical 6, the experiment to measure the speed of sound in air using a two channel oscilloscope, signal generator, microphone and loudspeaker, the following results were obtained for a signal of frequency 3 kHz:

Table 2 Data from the speed of sound experiment

Successive distances from the loudspeaker where the waves are in antiphase /cm

134.3 122.9 111.2 100.1 88.9 78.0 66.3 55.0

a) Use these data to calculate the mean wavelength of the sound, giving the uncertainty in this figure (3 marks)

b) Using the frequency given, calculate the speed of sound in air

(2 marks)

9 This question concerns the images formed by lenses.

a) Make a scale drawing to show how an image is formed by a diverging lens. The lens has a focal length of 10 cm, and the object is 5 cm from the centre of the lens. The object is 2 cm tall. Hint: the ray diagram will be much easier to draw if you use

squared paper. (4 marks)

b) Is the image real or virtual? Give a reason for your answer

(2 marks)

c) Use the lens formula, with the sign convention ‘real is positive’ and the given object distance and focal length to confirm that this image is in the correct place (2 marks)

d) Calculate the magnification, and compare it to the magnification measured from your drawing (2 marks) e) What is the power of this lens? (2 marks)

f) If you add a second lens to this, with a power of + 10 dioptres, what is the total power? (2 marks)

10 This question concerns refractive indices

The drawing (not to scale) shows a ray of light passing from water, through silica glass and into air.

a) Calculate the critical angle at the glass/air interface (2 marks)

b) Calculate the angle ?1 at the water/glass interface that will lead to the ray striking the glass/air interface at the critical angle

(4 marks)

11 The CD that was used in Assignment 1 was used to measure the wavelength of a green laser pointer. The spacing of the lines on the CD was 1.5 x 10-6 m.

The CD was placed 40 cm from a wall, and the distances from the central maximum of the green laser to the diffracted beam were measured to be:

Table 3 Measurements for Question 11

Distance from central maximum to the diffracted beam/ cm

15.5 15.5 15.2 15.6 15.7

Calculate the wavelength of the green laser (3 marks)

12 This question concerns polarisation.

a) Explain what is meant by polarisation of a wave. This should include a mention of which types of wave can, and which cannot,

be polarised (3 marks)

b) Explain why the two sheets of Polaroid pictured in the photographs below will both allow light through in one orientation, but when one is rotated by 90o light is no longer

transmitted. (4 marks)

Figure 2 Polaroid sheets oriented in the same way, and at right angles to one another

13 The bright light emitted by sodium lamps comes from a transition between electrons at an energy level of – 3.04 eV falling to an

energy level of -5.14 eV. Calculate the wavelength of the light emitted (2 marks) 14 A scanning electron microscope is operating with 25 keV electrons.

a) Calculate the energy, in J, possessed by the electrons (2 marks)

b) Calculate the velocity of the electron, given that the mass of an electron is 9.11 × 10-31 kg (2 marks) c) Calculate the momentum of the electrons (2 marks)

d) Hence calculate the wavelength of the electrons (2 marks)

e) What effect would increasing the electron energy have on the

wavelength, and what consequence would that have on the

resolution of the images? (2 marks)

In ultrasound, increasing the frequency improves the resolution of the image but,

f) what happens to the depth of the scan that you can obtain when the frequency is increased? (1 mark)

15 This question concerns the particulate nature of light.

a) Describe one experiment or observation that shows that light has wave properties and one experiment or observation that shows that it behaves as a stream of particles. Ensure that you explain precisely how each experiment leads to that conclusion.

(4 marks)

b) Green light of wavelength 550 nm is shone on potassium, which has a work function of 2.0 eV. Calculate the maximum kinetic energy of the photoelectrons emitted. (2 marks)

Total for the assignment 62 marks

Submit your assignment

When you have completed your assignment, submit it to your tutor for marking. Please convert your work into pdf format. Your tutor will send you helpful feedback and advice to help you progress through the course.

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