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

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

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

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

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

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

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

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

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.

1Measurements & Errors

1.1Measurements & Errors

1.1.1Use of SI Units

1.1.2SI Prefixes, Standard Form & Converting Units

1.1.3End of Topic Test - Units & Prefixes

1.1.4Limitation of Physical Measurements

1.1.5Uncertainty

1.1.6Estimation

1.1.7End of Topic Test - Measurements & Errors

2Particles & Radiation

2.1Particles

2.1.1Atomic Model

2.1.2Specific Charge, Protons & Neutron Numbers

2.1.3End of Topic Test - Atomic Model

2.1.4Isotopes

2.1.5Stable & Unstable Nuclei

2.1.6End of Topic Test - Isotopes & Nuclei

2.1.7A-A* (AO3/4) - Stable & Unstable Nuclei

2.1.8Particles, Antiparticles & Photons

2.1.9Particle Interactions

2.1.10Classification of Particles

2.1.11End of Topic Test - Particles & Interactions

2.1.12Quarks & Antiquarks

2.1.13Application of Conservation Laws

2.1.14End of Topic Test - Leptons & Quarks

2.1.15Exam-Style Question - Radioactive Decay

2.2Electromagnetic Radiation & Quantum Phenomena

2.2.1The Photoelectric Effect

2.2.2The Photoelectric Effect Explanation

2.2.3End of Topic Test - The Photoelectric Effect

2.2.4Collisions of Electrons with Atoms

2.2.5Energy Levels & Photon Emission

2.2.6Wave-Particle Duality

2.2.7End of Topic Test - Absorption & Emission

3Waves

3.1Progressive & Stationary Waves

3.1.1Progressive Waves

3.1.2Wave Speed & Phase Difference

3.1.3Longitudinal & Transverse Waves

3.1.4End of Topic Test - Progressive Waves

3.1.5Polarisation

3.1.6Stationary Waves

3.1.7Stationary Waves 2

3.1.8End of Topic Test - Polarisation & Stationary Wave

3.1.9A-A* (AO3/4) - Stationary Waves

3.2Refraction, Diffraction & Interference

3.2.1Interference

3.2.2Interference 2

3.2.3End of Topic Test - Interference

3.2.4Diffraction

3.2.5Diffraction Gratings

3.2.6End of Topic Test - Diffraction

3.2.7Refraction at a Plane Surface

3.2.8Internal Reflection & Fibre Optics

3.2.9End of Topic Test - Refraction

3.2.10Exam-Style Question - Waves

4Mechanics & Materials

4.1Force, Energy & Momentum

4.2Materials

4.2.1Density

4.2.2Bulk Properties of Solids

4.2.3Energy in Materials

4.2.4Young Modulus

4.2.5End of Topic Test - Materials

5Electricity

5.1Current Electricity

5.1.1Basics of Electricity

5.1.2Current-Voltage Characteristics

5.1.3End of Topic Test - Basics of Electricity

5.1.4Resistivity

5.1.5Superconductivity

5.1.6A-A* (AO3/4) - Superconductivity

5.1.7End of Topic Test - Resistivity & Superconductors

5.1.8Circuits

5.1.9Power and Conservation

5.1.10Potential Divider

5.1.11Emf & Internal Resistance

5.1.12End of Topic Test - Power & Potential

5.1.13Exam-Style Question - Resistance

6Further Mechanics & Thermal Physics (A2 only)

6.1Periodic Motion (A2 only)

6.1.1Circular Motion

6.1.2Circular Motion 2

6.1.3End of Topic Test - Circular Motion

6.1.4Simple Harmonic Motion

6.1.5Simple Harmonic Systems

6.1.6Energy in Simple Harmonic Motion

6.1.7Resonance

6.1.8End of Topic Test - Simple Harmonic Motion

6.1.9A-A* (AO3/4) - Simple Harmonic Motion

6.2Thermal Physics (A2 only)

6.2.1Thermal Energy Transfer

6.2.2Thermal Energy Transfer Experiments

6.2.3Ideal Gases

6.2.4Ideal Gases 2

6.2.5Boyle's Law & Charles' Law

6.2.6Molecular Kinetic Theory Model

6.2.7Molecular Kinetic Theory Model 2

6.2.8End of Topic Test - Thermal Energy & Ideal Gases

6.2.9Exam-Style Question - Ideal Gases

7Fields & Their Consequences (A2 only)

7.1Fields (A2 only)

7.1.1Fields

7.2Gravitational Fields (A2 only)

7.2.1Newton's Law

7.2.2Gravitational Field Strength

7.2.3Gravitational Potential

7.2.4Orbits of Planets & Satellites

7.2.5Escape Velocity & Synchronous Orbits

7.2.6End of Topic Test - Gravitational Fields

7.3Electric Fields (A2 only)

7.3.1Coulomb's Law

7.3.2Electric Field Strength

7.3.3Electric Field Strength 2

7.3.4Electric Potential

7.3.5End of Topic Test - Electric Fields

7.3.6A-A* (AO3/4) - Electric and Gravitational Field

7.4Capacitance (A2 only)

7.4.1Capacitance

7.4.2Parallel Plate Capacitor

7.4.3Energy Stored by a Capacitor

7.4.4Capacitor Discharge

7.4.5Capacitor Charge

7.5Magnetic Fields (A2 only)

7.5.1Magnetic Flux Density

7.5.2End of Topic Test - Capacitance & Flux Density

7.5.3Moving Charges in a Magnetic Field

7.5.4Magnetic Flux & Flux Linkage

7.5.5Electromagnetic Induction

7.5.6Electromagnetic Induction 2

7.5.7Alternating Currents

7.5.8Operation of a Transformer

7.5.9Magnetic Flux Density

7.5.10End of Topic Test - Electromagnetic Induction

8Nuclear Physics (A2 only)

8.1Radioactivity (A2 only)

8.1.1Rutherford Scattering

8.1.2Alpha & Beta Radiation

8.1.3Gamma Radiation

8.1.4Radioactive Decay

8.1.5Half Life

8.1.6End of Topic Test - Radioactivity

8.1.7Nuclear Instability

8.1.8Nuclear Radius

8.1.9Mass & Energy

8.1.10Binding Energy

8.1.11Induced Fission

8.1.12Safety Aspects of Nuclear Reactors

8.1.13End of Topic Test - Nuclear Physics

8.1.14A-A* (AO3/4) - Nuclear Fusion

9Option: Astrophysics (A2 only)

9.1Telescopes (A2 only)

9.1.1Astronomical Telescopes

9.1.2Reflecting Telescopes

9.1.3Single Dish Radio Telescopes

9.1.4Large Diameter Telescopes

9.2Classification of Stars (A2 only)

9.2.1Classification by Luminosity

9.2.2Absolute Magnitude

9.2.3Black Body Radiation

9.2.4Stellar Spectral Classes

9.2.5Hertzsprung-Russell Diagrams

9.2.6Astronomical Objects

9.3Cosmology (A2 only)

9.3.1Doppler Effect

9.3.2Hubble's Law

9.3.3Quasars

9.3.4Detecting Exoplanets

10Option: Medical Physics (A2 only)

10.1Physics of the Eye (A2 only)

10.1.1Physics of Vision

10.1.2Defects of Vision

10.1.3Lenses

10.1.4Correcting Defects of Vision

10.2Physics of the Ear (A2 only)

10.2.1Structure of the Ear

10.2.2Sensitivity of the Ear

10.2.3Hearing Defects

10.3Biological Measurement (A2 only)

10.3.1Electrocardiography (ECG)

10.4Non-Ionising Imaging (A2 only)

10.4.1Ultrasound Imaging

10.4.2Ultrasound Imaging 2

10.4.3Fibre Optics & Endoscopy

10.4.4Magnetic Resonance Scanning

10.5X-Ray Imaging (A2 only)

10.5.1Diagnostic X-Rays

10.5.2X-Ray Image Processing

10.5.3Absorption of X-Rays

10.5.4CT Scanners

10.6Radionuclide Imaging & Therapy (A2 only)

10.6.1Imaging Techniques

10.6.2Half Life

10.6.3Gamma Camera

10.6.4High Energy X-Rays

10.6.5Radioactive Implants

10.6.6Imaging Comparisons

11Option: Engineering Physics (A2 only)

11.1Rotational Dynamics (A2 only)

11.1.1Moment of Inertia

11.1.2Rotational Kinetic Energy

11.1.3Rotational Motion

11.1.4Torque & Angular Acceleration

11.1.5Angular Momentum

11.1.6Angular Work & Power

11.2Thermodynamics & Engines (A2 only)

11.2.1First Law of Thermodynamics

11.2.2Non-Flow Processes

11.2.3p-V Diagrams

11.2.4Engine Cycles

11.2.5Second Law & Engines

11.2.6Reversed Heat Engines

12Option: Turning Points in Physics (A2 only)

12.1Discovery of the Electron (A2 only)

12.1.1Cathode Rays

12.1.2Thermionic Electron Emission

12.1.3Electron Specific Charge

12.1.4Millikan's Experiment

12.2Wave-Particle Duality (A2 only)

12.2.1Newton's & Huygen's Theories of Light

12.2.2Electromagnetic Waves

12.2.3Photoelectricity

12.2.4Wave-Particle Duality

12.2.5Electron Microscopes

12.3Special Relativity (A2 only)

12.3.1Michelson-Morley Experiment

12.3.2Einstein's Theory of Special Relativity

12.3.3Time Dilation

12.3.4Length Contraction

12.3.5Mass & Energy

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