3.2.5

Diffraction Gratings

Test yourself on Diffraction Gratings

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Diffraction Grating Equation

The pattern produced by a diffraction grating can be described by the diffraction grating equation.

Equation

Equation

Diffraction gratings produce a pattern which is described by:
- $d\sin\theta = n\lambda$
  - Where d is the distance between slits in the grating, θ is the angle between the maximum and the zero order line, λ is the wavelength of incident light, and n is the order of the maximum.

Slit spacing

Slit spacing

A diffraction grating is made of many slits.
If there are 1000 slits per metre, then slit spacing is 1/1000 metres.
In general, if there are x slits per metre, then the slit spacing is 1/x metres.
This gives the value of "d".

Orders

Orders

The variable "n" stands for the order of the maximum.
Knowing d and λ lets us predict the angle of the central maximum.
The central maximum is the zero order. "n" is zero.
This implies that θ is zero. This is what we expect.
The first order maximum will have n = 1, the second order maximum will have n = 2, and so on.

Not all orders exist

Not all orders exist

Remember that sin θ cannot be greater than 1.
- If you are using the equation and find that sin θ is larger than 1, the order you are looking at must not exist.

Conclusions

Conclusions

As we increase λ, sin θ increases so θ increases. This means the pattern becomes more spread out.
If we increase the distance between slits, d, sin θ decreases so θ decreased. This means the pattern becomes less spread out.

Derivation of Grating Equation

You need to know how to derive the diffraction grating equation.

Step 1 - producing coherent sources

Step 1 - producing coherent sources

Light enters the grating as parallel rays.
It diffracts through each slit.
The slits then act as coherent (in phase) and monochromatic (same wavelength) sources of light.
These diffracted waves then interfere with each other to produce the pattern.

Step 2 - angle to 1st order

Step 2 - angle to 1st order

The 1st order maximum happens at an angle such that the path difference between two sources is one wavelength, λ (for constructive interference).
Let's call this angle θ.

Step 3 - create triangle

Step 3 - create triangle

We create a triangle as shown above.
We know the distance between the two slits is d.
We know the path difference is λ.
We know the angle θ by geometry.

Step 4 - use trigonometry

Step 4 - use trigonometry

Using trigonometry, we can see that:
- path difference $=\lambda = d \sin\theta$

Step 5 - generalise for all n

Step 5 - generalise for all n

We know that maxima always occur for when the path difference is a whole number multiple of λ (constructive interference).
Therefore, we can generalise the equation so that path difference = nλ
- $n\lambda = d \sin \theta$

Applications of Diffraction Gratings

Diffraction gratings are very useful for physicists.

Analysing light

Analysing light

Diffraction gratings can be used to separate wavelengths in light from different substances.
The wavelengths present can help us learn new things about the substance being tested.

Atomic spacing in crystals

Atomic spacing in crystals

Atoms in a crystal can act like a diffraction grating, with little gaps for light to pass through.
We can find the spacing between the atoms in the crystal by looking at how X-rays diffract through the crystal.

1

Measurements & Errors

1.1

Measurements & Errors

1.1.1SI Base Units 1.1.2Combining SI Units 1.1.3Prefixes of Units 1.1.4Standard Form 1.1.5Converting Units 1.1.6End of Topic Test - Units & Prefixes 1.1.7Limitation of Physical Measurements 1.1.8Uncertainty 1.1.9Estimation 1.1.10End of Topic Test - Measurements & Errors 1.1.11Diagnostic Misconceptions - Converting between SI 1.1.12Diagnostic Misconceptions - SI & Area/Volume

2

Particles & Radiation

2.1

Particles

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

2.2

Electromagnetic 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 2.2.8Diagnostic Misconceptions - Electron Volts 2.2.9Diagnostic Misconceptions - Converting eV & Joules

3

Waves

3.1

Progressive & 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

3.2

Refraction, 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

4

Mechanics & Materials

4.1

Force, Energy & Momentum

4.1.1Scalars & Vectors 4.1.2Vector Problems 4.1.3End of Topic Test - Scalars & Vectors 4.1.4Moments 4.1.5Centre of Mass 4.1.6End of Topic Test - Moments & Centre of Mass 4.1.7Motion in a Straight Line 4.1.8Graphs of Motion 4.1.9Bouncing Ball Example 4.1.10End of Topic Test - Motion in a Straight Line 4.1.11Acceleration Due to Gravity 4.1.12Projectile Motion 4.1.13Friction 4.1.14Terminal Speed 4.1.15End of Topic Test - Acceleration Due to Gravity 4.1.16Newton's Laws 4.1.17Momentum 4.1.18Momentum 2 4.1.19End of Topic Test - Newton's Laws & Momentum 4.1.20A-A* (AO3/4) - Newton's Third Law 4.1.21Work & Energy 4.1.22Power & Efficiency 4.1.23Conservation of Energy 4.1.24End of Topic Test - Work, Energy & Power 4.1.25Exam-Style Question - Forces 4.1.26Diagnostic Misconceptions - Perpendicular Vectors 4.1.27Diagnostic Misconceptions - Weight Acts Downwards 4.1.28Diagnostic Misconceptions - Acceleration Direction 4.1.29Diagnostic Misconceptions - Stationary Objects 4.1.30Diagnostic Misconceptions - Action & Reaction 4.1.31Diagnostic Misconceptions - RF Direction 4.1.32Diagnostic Misconceptions - RF Acceleration 4.1.33Diagnostic Misconceptions - Change in Momentum

4.2

Materials

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

5

Electricity

5.1

Current 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 5.1.14Diagnostic Misconceptions - Constant Current 5.1.15Diagnostic Misconceptions - Potential Difference

6

Further Mechanics & Thermal Physics (A2 only)

7

Fields & Their Consequences (A2 only)

7.1

Fields (A2 only)

7.2

Gravitational 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

7.3

Electric 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

7.4

Capacitance (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

7.5

Magnetic 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

8

Nuclear Physics (A2 only)

8.1

Radioactivity (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

9

Option: Astrophysics (A2 only)

9.1

Telescopes (A2 only)

9.1.1Astronomical Telescopes 9.1.2Reflecting Telescopes 9.1.3Single Dish Radio Telescopes 9.1.4Large Diameter Telescopes

9.2

Classification 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

9.3

Cosmology (A2 only)

9.3.1Doppler Effect 9.3.2Hubble's Law 9.3.3Quasars 9.3.4Detecting Exoplanets

10

Option: Medical Physics (A2 only)

10.1

Physics of the Eye (A2 only)

10.1.1Physics of Vision 10.1.2Defects of Vision 10.1.3Lenses 10.1.4Correcting Defects of Vision

10.2

Physics of the Ear (A2 only)

10.2.1Structure of the Ear 10.2.2Sensitivity of the Ear 10.2.3Hearing Defects

10.3

Biological Measurement (A2 only)

10.3.1Electrocardiography (ECG)

10.4

Non-Ionising Imaging (A2 only)

10.4.1Ultrasound Imaging 10.4.2Ultrasound Imaging 2 10.4.3Fibre Optics & Endoscopy 10.4.4Magnetic Resonance Scanning

10.5

X-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

10.6

Radionuclide 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

11

Option: Engineering Physics (A2 only)

11.1

Rotational 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

11.2

Thermodynamics & 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

12

Option: Turning Points in Physics (A2 only)

12.1

Discovery of the Electron (A2 only)

12.1.1Cathode Rays 12.1.2Thermionic Electron Emission 12.1.3Electron Specific Charge 12.1.4Millikan's Experiment

12.2

Wave-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

12.3

Special 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

Jump to other topics

1

Measurements & Errors

1.1

Measurements & Errors

1.1.1SI Base Units 1.1.2Combining SI Units 1.1.3Prefixes of Units 1.1.4Standard Form 1.1.5Converting Units 1.1.6End of Topic Test - Units & Prefixes 1.1.7Limitation of Physical Measurements 1.1.8Uncertainty 1.1.9Estimation 1.1.10End of Topic Test - Measurements & Errors 1.1.11Diagnostic Misconceptions - Converting between SI 1.1.12Diagnostic Misconceptions - SI & Area/Volume

2

Particles & Radiation

2.1

Particles

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

2.2

Electromagnetic 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 2.2.8Diagnostic Misconceptions - Electron Volts 2.2.9Diagnostic Misconceptions - Converting eV & Joules

3

Waves

3.1

Progressive & 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

3.2

Refraction, 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

4

Mechanics & Materials

4.1

Force, Energy & Momentum

4.1.1Scalars & Vectors 4.1.2Vector Problems 4.1.3End of Topic Test - Scalars & Vectors 4.1.4Moments 4.1.5Centre of Mass 4.1.6End of Topic Test - Moments & Centre of Mass 4.1.7Motion in a Straight Line 4.1.8Graphs of Motion 4.1.9Bouncing Ball Example 4.1.10End of Topic Test - Motion in a Straight Line 4.1.11Acceleration Due to Gravity 4.1.12Projectile Motion 4.1.13Friction 4.1.14Terminal Speed 4.1.15End of Topic Test - Acceleration Due to Gravity 4.1.16Newton's Laws 4.1.17Momentum 4.1.18Momentum 2 4.1.19End of Topic Test - Newton's Laws & Momentum 4.1.20A-A* (AO3/4) - Newton's Third Law 4.1.21Work & Energy 4.1.22Power & Efficiency 4.1.23Conservation of Energy 4.1.24End of Topic Test - Work, Energy & Power 4.1.25Exam-Style Question - Forces 4.1.26Diagnostic Misconceptions - Perpendicular Vectors 4.1.27Diagnostic Misconceptions - Weight Acts Downwards 4.1.28Diagnostic Misconceptions - Acceleration Direction 4.1.29Diagnostic Misconceptions - Stationary Objects 4.1.30Diagnostic Misconceptions - Action & Reaction 4.1.31Diagnostic Misconceptions - RF Direction 4.1.32Diagnostic Misconceptions - RF Acceleration 4.1.33Diagnostic Misconceptions - Change in Momentum

4.2

Materials

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

5

Electricity

5.1

Current 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 5.1.14Diagnostic Misconceptions - Constant Current 5.1.15Diagnostic Misconceptions - Potential Difference

6

Further Mechanics & Thermal Physics (A2 only)

7

Fields & Their Consequences (A2 only)

7.1

Fields (A2 only)

7.2

Gravitational 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

7.3

Electric 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

7.4

Capacitance (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

7.5

Magnetic 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

8

Nuclear Physics (A2 only)

8.1

Radioactivity (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

9

Option: Astrophysics (A2 only)

9.1

Telescopes (A2 only)

9.1.1Astronomical Telescopes 9.1.2Reflecting Telescopes 9.1.3Single Dish Radio Telescopes 9.1.4Large Diameter Telescopes

9.2

Classification 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

9.3

Cosmology (A2 only)

9.3.1Doppler Effect 9.3.2Hubble's Law 9.3.3Quasars 9.3.4Detecting Exoplanets

10

Option: Medical Physics (A2 only)

10.1

Physics of the Eye (A2 only)

10.1.1Physics of Vision 10.1.2Defects of Vision 10.1.3Lenses 10.1.4Correcting Defects of Vision

10.2

Physics of the Ear (A2 only)

10.2.1Structure of the Ear 10.2.2Sensitivity of the Ear 10.2.3Hearing Defects

10.3

Biological Measurement (A2 only)

10.3.1Electrocardiography (ECG)

10.4

Non-Ionising Imaging (A2 only)

10.4.1Ultrasound Imaging 10.4.2Ultrasound Imaging 2 10.4.3Fibre Optics & Endoscopy 10.4.4Magnetic Resonance Scanning

10.5

X-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

10.6

Radionuclide 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

11

Option: Engineering Physics (A2 only)

11.1

Rotational 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

11.2

Thermodynamics & 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

12

Option: Turning Points in Physics (A2 only)

12.1

Discovery of the Electron (A2 only)

12.1.1Cathode Rays 12.1.2Thermionic Electron Emission 12.1.3Electron Specific Charge 12.1.4Millikan's Experiment

12.2

Wave-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

12.3

Special 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

Practice questions on Diffraction Gratings

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1
What is the correct equation for a diffraction grating?Multiple choice
2
What is the equation for the path difference at the first order maximum?Multiple choice
3
Which of these roles can a diffraction grating perform?Multiple choice
4
Uses of diffraction gratings:Fill in the list

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Diffraction

End of Topic Test - Diffraction