Diffraction Gratings

Test yourself

Diffraction Grating Equation

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

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

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

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

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

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

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

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

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

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
- $n\lambda = d \sin \theta$

1Principles of Science I

1.1Structure & 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

1.2Properties 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

1.3Cell 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

1.4Cell Specialisation

1.4.1Cell Specialisation

1.4.2Blood Cells

1.4.3Plant Cells

1.4.4Gametes

1.5Tissue 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

1.6Working 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

1.7Waves 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

2Practical Scientific Procedures and Techniques

2.1Titration

2.1.1pH Curves & Titrations

2.1.2pH Curves & Titrations 2

2.1.3Buffer Solutions

2.2Colorimetry

2.2.1Measuring Rates

2.2.2Beer-Lambert Law

2.3Chromatography

2.3.1Overview of Chromatography

2.3.2Thin-Layer Chromatography

2.3.3Column Chromatography

2.3.4Gas Chromatography

3Science Investigation Skills

3.1Scientific 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

3.2Data Handling & Analysis

3.2.1Types of Data

3.2.2Descriptive Statistics

3.2.3Presentation & Display of Data

3.3Enzymes in Action

3.3.1Overview of Protein Structure

3.3.2Enzymes

3.3.3Factors Affecting Enzyme Activity

3.3.4Enzyme-Controlled Reactions

3.4Diffusion

3.4.1Diffusion

3.5Plants & Their Environment

3.5.1Factors Affecting Plant Growth

3.5.2Measuring Number & Distribution of Species

3.6Energy Content in Fuels

3.6.1Fractions

3.6.2Burning Hydrocarbons

3.6.3Combustion

3.6.4Energy

3.6.5Energy at Home

3.6.6Calorimetry

3.7Electrical 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

4Principles of Science II

4.1Extracting Elements

4.1.1Atom Economy

4.2Relating 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

4.3Organic 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

4.4Energy Changes in Industry

4.4.1The Kelvin Scale

4.4.2Enthalpy Changes

4.4.3Calorimetry

4.4.4Bond Enthalpies

4.4.5Hess' Law

4.5The 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

4.6Ventilation & 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

4.7Urinary 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

4.8Cell Transport

4.8.1Cell Membrane Structure

4.8.2Diffusion

4.8.3Osmosis

4.8.4Active Transport

4.9Thermal 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

4.10Materials

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

4.11Fluids

4.11.1Fluid Flow

4.11.2Viscosity

4.11.3Density

4.11.4Continuity Equation

4.11.5Bernoulli's Equation

4.11.6Non-Newtonian Fluids

5Contemporary Issues in Science

5.1Contemporary 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

5.2Analysing Scientific Information

5.2.1Validity

5.2.2Peer Review

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