1.6.7

Interference

Test yourself on Interference

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Path Difference and Coherence

To understand interference and diffraction patterns, it is important to understand path difference and coherence.

Coherence

Coherence

Interference happens when any two waves are superimposed on one another.
- But in most cases, this creates a very messy wave pattern.
To see a clear interference pattern, we need two waves that are coherent.
Coherent means that the two waves must have the same frequency and wavelength, and have a fixed phase relation.
- Usually this fixed phase relation is zero.

Path difference

Path difference

The path difference between two waves is the difference in length travelled by the waves to get to a certain point.

Path difference and interference

Path difference and interference

For two coherent wave sources:
If the path difference is a multiple of λ, the waves will be in phase and we will see constructive interference:
- Path difference $= nλ$
If the path difference is a whole number plus a half λ, the waves will be exactly out of phase and we will see destructive interference:
- Path difference $= (n+\frac{1}2)\lambda$

Young's Double-Slit Experiment

Young's famous double-slit experiment deals with the interference from two monochromatic, coherent sources. Monochromatic means all light is of the same wavelength.

Producing coherent waves

Producing coherent waves

To observe interference between two waves, we need two coherent sources.
We can use two separate sources for this - but it is often tricky to make sure they are coherent.
A useful trick is to shine a laser through two slits.
- The laser produces monochromatic, coherent light.
- The two slits then act like two identical sources of laser light.
- The slits must have the same size and be comparable to the wavelength of the laser light to diffract it.

Experiment layout

Experiment layout

The diagram shows the production and interference of two coherent, monochromatic light waves.
This produces a series of light and dark fringes corresponding to constructive and destructive interference.

Fringes in Young's Double Slit Experiment

We can calculate the spacing of fringes seen in the double-slit experiment.

Fringe spacing

Fringe spacing

To calculate the spacing between bright fringes in the double-slit experiment, use the following equation:
- $w = \frac{\lambda D}{s}$
  - Where the fringe spacing is w, the wavelength is λ, the spacing between slits is s, and the distance from the slits to the screen is D.

Average over many fringes

Average over many fringes

Normally, the fringe spacing is very small.
- To ensure our measurement is accurate we measure across lots of fringes and divide by the number of fringe widths to find an average.

Using white light

Using white light

We can use white light instead of laser light in a double slit experiment.
Instead of clear bright and dark fringes:
- The middle fringe is just bright white light.
- All fringes are more spread out.
- Side fringes have a spectrum of visible colours. Blue light diffracts less than red so is nearer the centre of the screen.

1

Principles of Science I

1.1

Structure & Bonding

1.1.1Atomic Model 1.1.2Electron Shells, Sub-Shells & Orbitals 1.1.3Ionic Bonding 1.1.4Representing Ionic Bonds 1.1.5Covalent Bonding 1.1.6Representing Covalent Bonds 1.1.7Metallic Bonding 1.1.8Intermolecular Forces 1.1.9Intermolecular Forces 2 1.1.10End of Topic Test - Bonding 1.1.11Relative Masses 1.1.12The Mole 1.1.13Molar Calculations 1.1.14Molar Calculations 2 1.1.15Empirical & Molecular Formulae 1.1.16Balanced Equations 1.1.17Percentage Yield 1.1.18End of Topic Test - Amount of Substance

1.2

Properties of Substances

1.2.1The Periodic Table 1.2.2Ionisation Energy 1.2.3Factors Affecting Ionisation Energies 1.2.4Trends of Ionisation 1.2.5Trends in the Periodic Table 1.2.6Polarity 1.2.7Metals & Non-Metals 1.2.8Alkali Metals 1.2.9Alkaline Earth Metals 1.2.10Reactivity of Alkaline Earth Metals 1.2.11Redox 1.2.12Transition Metals 1.2.13Redox Reactions of Transition Metals

1.3

Cell Structure & Function

1.3.1Introduction to Cells 1.3.2Prokaryotes 1.3.3Organelles of Eukaryotic Cells 1.3.4Organelles of Eukaryotic Cells 2 1.3.5Organelles in Plant Cells 1.3.6Microscopy 1.3.7End of Topic Test - Cell Structure

1.4

Cell Specialisation

1.4.1Cell Specialisation 1.4.2Blood Cells 1.4.3Plant Cells 1.4.4Gametes

1.5

Tissue Structure & Function

1.5.1Human Gas Exchange 1.5.2Blood Vessels 1.5.3Atherosclerosis 1.5.4Skeletal Muscle 1.5.5Slow & Fast Twitch Fibres 1.5.6Neurones 1.5.7Speed of Transmission 1.5.8Action Potentials 1.5.9End of Topic Test - Neurones & Action Potentials 1.5.10Synapses 1.5.11Types of Synapse 1.5.12Medical Application 1.5.13End of Topic Test - Synapses 1.5.14Chemical Brain Imbalances 1.5.15Effect of Drugs on the Brain

1.6

Working with Waves

1.6.1Progressive Waves 1.6.2Wave Speed & Phase Difference 1.6.3Longitudinal & Transverse Waves 1.6.4Stationary Waves 1.6.5Stationary Waves 2 1.6.6Applications of Stationary Waves 1.6.7Interference 1.6.8Diffraction 1.6.9Diffraction Gratings 1.6.10Application of Diffraction Gratings

1.7

Waves in Communication

1.7.1Refraction at a Plane Surface 1.7.2Internal Reflection & Fibre Optics 1.7.3Applications of Total Internal Reflection 1.7.4Properties 1.7.5Gamma, X-Ray & UV Light 1.7.6Visible Light 1.7.7Infrared, Microwave & Radio Waves 1.7.8Intensity 1.7.9Digital & Analogue Signals 1.7.10Communication Channels

2

Practical Scientific Procedures and Techniques

2.1

Titration

2.1.1pH Curves & Titrations 2.1.2pH Curves & Titrations 2 2.1.3Buffer Solutions

2.2

Colorimetry

2.2.1Measuring Rates 2.2.2Beer-Lambert Law

2.3

Chromatography

2.3.1Overview of Chromatography 2.3.2Thin-Layer Chromatography 2.3.3Column Chromatography 2.3.4Gas Chromatography

3

Science Investigation Skills

3.1

Scientific Processes

3.1.1Aims, Hypotheses & Sampling 3.1.2Pilot Studies & Design 3.1.3Ethics 3.1.4Variables & Control 3.1.5Demand Characteristics & Investigator Effects 3.1.6Features of Science 3.1.7Scientific Report 3.1.8Scientific Report 2

3.2

Data Handling & Analysis

3.2.1Types of Data 3.2.2Descriptive Statistics 3.2.3Presentation & Display of Data

3.3

Enzymes in Action

3.3.1Overview of Protein Structure 3.3.2Enzymes 3.3.3Factors Affecting Enzyme Activity 3.3.4Enzyme-Controlled Reactions

3.4

Diffusion

3.5

Plants & Their Environment

3.5.1Factors Affecting Plant Growth 3.5.2Measuring Number & Distribution of Species

3.6

Energy Content in Fuels

3.6.1Fractions 3.6.2Burning Hydrocarbons 3.6.3Combustion 3.6.4Energy 3.6.5Energy at Home 3.6.6Calorimetry

3.7

Electrical Circuits

3.7.1Circuit Diagrams & Components 3.7.2Diodes, LDRs & Thermistors 3.7.3Resistance 3.7.4Electrical Work 3.7.5Ohm's Law 3.7.6Domestic Uses of Electricity 3.7.7Fuses

4

Principles of Science II

4.1

Extracting Elements

4.1.1Atom Economy

4.2

Relating Properties to use of Substances

4.2.1Group 2 Chemistry 4.2.2End of Topic Test - Group 2 4.2.3Electrolysis 4.2.4Electrolysis Examples 4.2.5Extracting Metals 4.2.6Transition Metals 4.2.7Variable Oxidation States 4.2.8Heterogeneous Catalysts 4.2.9Homogeneous Catalysts

4.3

Organic Chemistry

4.3.1Naming Compounds 4.3.2Functional Groups 4.3.3Isomerism 4.3.4Hydrocarbons 4.3.5Structure of Alkanes 4.3.6Boiling Points of Alkanes 4.3.7Alkenes 4.3.8Curly Arrows & Mechanisms 4.3.9Cracking 4.3.10Combustion 4.3.11Free Radical Substitution of Alkanes 4.3.12Electrophilic Addition of Alkenes

4.4

Energy Changes in Industry

4.4.1The Kelvin Scale 4.4.2Enthalpy Changes 4.4.3Calorimetry 4.4.4Bond Enthalpies 4.4.5Hess' Law

4.5

The Circulatory System

4.5.1The Circulatory System 4.5.2Blood Vessels 4.5.3Blood Transfusion & the ABO Rhesus System 4.5.4The Heart 4.5.5The Cardiac Cycle 4.5.6Cardiac Output 4.5.7Coordination of Heart Action 4.5.8Heart Dissection 4.5.9Controlling Heart Rate 4.5.10Electrocardiograms 4.5.11Cardiovascular Disease 4.5.12Investigating Heart Rates

4.6

Ventilation & Gas Exchange

4.6.1Human Gas Exchange 4.6.2Ventilation 4.6.3Measuring Gas Exchange 4.6.4Controlling Ventilation Rate 4.6.5Lung Disease 4.6.6Lung Disease Data

4.7

Urinary System

4.7.1Kidneys & Control of Water Balance 4.7.2Kidneys & Osmoregulation 4.7.3Kidneys & Blood Pressure 4.7.4Urine 4.7.5Kidney Failure & Urinalysis 4.7.6Dialysis 4.7.7Transplants

4.8

Cell Transport

4.8.1Cell Membrane Structure 4.8.2Diffusion 4.8.3Osmosis 4.8.4Active Transport

4.9

Thermal Physics

4.9.1Power & Efficiency 4.9.2Work & Energy 4.9.3Conservation of Energy 4.9.4Pressure 4.9.5First Law of Thermodynamics 4.9.6Second Law of Thermodynamics 4.9.7Heat Engines, Heat Pumps & Refrigerators 4.9.8Non-Flow Processes 4.9.9p-V Diagrams 4.9.10Ideal Gases 4.9.11Ideal Gases 2 4.9.12Thermal Energy Transfer 4.9.13Thermal Energy Transfer Experiments

4.10

Materials

4.10.1Density 4.10.2Stress & Strain 4.10.3Properties of Materials 4.10.4Elasticity 4.10.5Plasticity 4.10.6Energy in Materials 4.10.7Young Modulus

4.11

Fluids

4.11.1Fluid Flow 4.11.2Viscosity 4.11.3Density 4.11.4Continuity Equation 4.11.5Bernoulli's Equation 4.11.6Non-Newtonian Fluids

5

Contemporary Issues in Science

5.1

Contemporary Issues in Science

5.1.1Sustainability 5.1.2Genetic Engineering 5.1.3Uses of Genetic Modification 5.1.4Stem Cell Therapy 5.1.5Cloning 5.1.6Cloning 2 5.1.7Nanotechnology 5.1.8Ecosystems

5.2

Analysing Scientific Information

5.2.1Validity 5.2.2Peer Review

Jump to other topics

1

Principles of Science I

1.1

Structure & Bonding

1.1.1Atomic Model 1.1.2Electron Shells, Sub-Shells & Orbitals 1.1.3Ionic Bonding 1.1.4Representing Ionic Bonds 1.1.5Covalent Bonding 1.1.6Representing Covalent Bonds 1.1.7Metallic Bonding 1.1.8Intermolecular Forces 1.1.9Intermolecular Forces 2 1.1.10End of Topic Test - Bonding 1.1.11Relative Masses 1.1.12The Mole 1.1.13Molar Calculations 1.1.14Molar Calculations 2 1.1.15Empirical & Molecular Formulae 1.1.16Balanced Equations 1.1.17Percentage Yield 1.1.18End of Topic Test - Amount of Substance

1.2

Properties of Substances

1.2.1The Periodic Table 1.2.2Ionisation Energy 1.2.3Factors Affecting Ionisation Energies 1.2.4Trends of Ionisation 1.2.5Trends in the Periodic Table 1.2.6Polarity 1.2.7Metals & Non-Metals 1.2.8Alkali Metals 1.2.9Alkaline Earth Metals 1.2.10Reactivity of Alkaline Earth Metals 1.2.11Redox 1.2.12Transition Metals 1.2.13Redox Reactions of Transition Metals

1.3

Cell Structure & Function

1.3.1Introduction to Cells 1.3.2Prokaryotes 1.3.3Organelles of Eukaryotic Cells 1.3.4Organelles of Eukaryotic Cells 2 1.3.5Organelles in Plant Cells 1.3.6Microscopy 1.3.7End of Topic Test - Cell Structure

1.4

Cell Specialisation

1.4.1Cell Specialisation 1.4.2Blood Cells 1.4.3Plant Cells 1.4.4Gametes

1.5

Tissue Structure & Function

1.5.1Human Gas Exchange 1.5.2Blood Vessels 1.5.3Atherosclerosis 1.5.4Skeletal Muscle 1.5.5Slow & Fast Twitch Fibres 1.5.6Neurones 1.5.7Speed of Transmission 1.5.8Action Potentials 1.5.9End of Topic Test - Neurones & Action Potentials 1.5.10Synapses 1.5.11Types of Synapse 1.5.12Medical Application 1.5.13End of Topic Test - Synapses 1.5.14Chemical Brain Imbalances 1.5.15Effect of Drugs on the Brain

1.6

Working with Waves

1.6.1Progressive Waves 1.6.2Wave Speed & Phase Difference 1.6.3Longitudinal & Transverse Waves 1.6.4Stationary Waves 1.6.5Stationary Waves 2 1.6.6Applications of Stationary Waves 1.6.7Interference 1.6.8Diffraction 1.6.9Diffraction Gratings 1.6.10Application of Diffraction Gratings

1.7

Waves in Communication

1.7.1Refraction at a Plane Surface 1.7.2Internal Reflection & Fibre Optics 1.7.3Applications of Total Internal Reflection 1.7.4Properties 1.7.5Gamma, X-Ray & UV Light 1.7.6Visible Light 1.7.7Infrared, Microwave & Radio Waves 1.7.8Intensity 1.7.9Digital & Analogue Signals 1.7.10Communication Channels

2

Practical Scientific Procedures and Techniques

2.1

Titration

2.1.1pH Curves & Titrations 2.1.2pH Curves & Titrations 2 2.1.3Buffer Solutions

2.2

Colorimetry

2.2.1Measuring Rates 2.2.2Beer-Lambert Law

2.3

Chromatography

2.3.1Overview of Chromatography 2.3.2Thin-Layer Chromatography 2.3.3Column Chromatography 2.3.4Gas Chromatography

3

Science Investigation Skills

3.1

Scientific Processes

3.1.1Aims, Hypotheses & Sampling 3.1.2Pilot Studies & Design 3.1.3Ethics 3.1.4Variables & Control 3.1.5Demand Characteristics & Investigator Effects 3.1.6Features of Science 3.1.7Scientific Report 3.1.8Scientific Report 2

3.2

Data Handling & Analysis

3.2.1Types of Data 3.2.2Descriptive Statistics 3.2.3Presentation & Display of Data

3.3

Enzymes in Action

3.3.1Overview of Protein Structure 3.3.2Enzymes 3.3.3Factors Affecting Enzyme Activity 3.3.4Enzyme-Controlled Reactions

3.4

Diffusion

3.5

Plants & Their Environment

3.5.1Factors Affecting Plant Growth 3.5.2Measuring Number & Distribution of Species

3.6

Energy Content in Fuels

3.6.1Fractions 3.6.2Burning Hydrocarbons 3.6.3Combustion 3.6.4Energy 3.6.5Energy at Home 3.6.6Calorimetry

3.7

Electrical Circuits

3.7.1Circuit Diagrams & Components 3.7.2Diodes, LDRs & Thermistors 3.7.3Resistance 3.7.4Electrical Work 3.7.5Ohm's Law 3.7.6Domestic Uses of Electricity 3.7.7Fuses

4

Principles of Science II

4.1

Extracting Elements

4.1.1Atom Economy

4.2

Relating Properties to use of Substances

4.2.1Group 2 Chemistry 4.2.2End of Topic Test - Group 2 4.2.3Electrolysis 4.2.4Electrolysis Examples 4.2.5Extracting Metals 4.2.6Transition Metals 4.2.7Variable Oxidation States 4.2.8Heterogeneous Catalysts 4.2.9Homogeneous Catalysts

4.3

Organic Chemistry

4.3.1Naming Compounds 4.3.2Functional Groups 4.3.3Isomerism 4.3.4Hydrocarbons 4.3.5Structure of Alkanes 4.3.6Boiling Points of Alkanes 4.3.7Alkenes 4.3.8Curly Arrows & Mechanisms 4.3.9Cracking 4.3.10Combustion 4.3.11Free Radical Substitution of Alkanes 4.3.12Electrophilic Addition of Alkenes

4.4

Energy Changes in Industry

4.4.1The Kelvin Scale 4.4.2Enthalpy Changes 4.4.3Calorimetry 4.4.4Bond Enthalpies 4.4.5Hess' Law

4.5

The Circulatory System

4.5.1The Circulatory System 4.5.2Blood Vessels 4.5.3Blood Transfusion & the ABO Rhesus System 4.5.4The Heart 4.5.5The Cardiac Cycle 4.5.6Cardiac Output 4.5.7Coordination of Heart Action 4.5.8Heart Dissection 4.5.9Controlling Heart Rate 4.5.10Electrocardiograms 4.5.11Cardiovascular Disease 4.5.12Investigating Heart Rates

4.6

Ventilation & Gas Exchange

4.6.1Human Gas Exchange 4.6.2Ventilation 4.6.3Measuring Gas Exchange 4.6.4Controlling Ventilation Rate 4.6.5Lung Disease 4.6.6Lung Disease Data

4.7

Urinary System

4.7.1Kidneys & Control of Water Balance 4.7.2Kidneys & Osmoregulation 4.7.3Kidneys & Blood Pressure 4.7.4Urine 4.7.5Kidney Failure & Urinalysis 4.7.6Dialysis 4.7.7Transplants

4.8

Cell Transport

4.8.1Cell Membrane Structure 4.8.2Diffusion 4.8.3Osmosis 4.8.4Active Transport

4.9

Thermal Physics

4.9.1Power & Efficiency 4.9.2Work & Energy 4.9.3Conservation of Energy 4.9.4Pressure 4.9.5First Law of Thermodynamics 4.9.6Second Law of Thermodynamics 4.9.7Heat Engines, Heat Pumps & Refrigerators 4.9.8Non-Flow Processes 4.9.9p-V Diagrams 4.9.10Ideal Gases 4.9.11Ideal Gases 2 4.9.12Thermal Energy Transfer 4.9.13Thermal Energy Transfer Experiments

4.10

Materials

4.10.1Density 4.10.2Stress & Strain 4.10.3Properties of Materials 4.10.4Elasticity 4.10.5Plasticity 4.10.6Energy in Materials 4.10.7Young Modulus

4.11

Fluids

4.11.1Fluid Flow 4.11.2Viscosity 4.11.3Density 4.11.4Continuity Equation 4.11.5Bernoulli's Equation 4.11.6Non-Newtonian Fluids

5

Contemporary Issues in Science

5.1

Contemporary Issues in Science

5.1.1Sustainability 5.1.2Genetic Engineering 5.1.3Uses of Genetic Modification 5.1.4Stem Cell Therapy 5.1.5Cloning 5.1.6Cloning 2 5.1.7Nanotechnology 5.1.8Ecosystems

5.2

Analysing Scientific Information

5.2.1Validity 5.2.2Peer Review

Practice questions on Interference

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1
What is the path difference?Multiple choice
2
Conditions for interference:Fill in the list
3
Why do we only use one source for Young's double slit experiment?Multiple choice
4
What are the conditions for interference?Fill in the list
5
What is the equation for the fringe separation in Young's double slit experiment?Multiple choice

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Applications of Stationary Waves

Diffraction