8.1.9

Diffraction Gratings

Test yourself on Diffraction Gratings

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

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:
    • dsin⁡θ=nλd\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 =λ=dsin⁡θ=\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
    • nλ=dsin⁡θn\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.
Jump to other topics
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Diffraction Gratings

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

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

Unlock your full potential with Seneca Premium

  • Unlimited access to 10,000+ open-ended exam questions

  • Mini-mock exams based on your study history

  • Unlock 800+ premium courses & e-books

Get started with Seneca Premium

Diffraction

End of Topic Test - Diffraction