The Diffraction Grating Equation (Edexcel International A Level Physics)

Revision Note

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Lindsay Gilmour



The Diffraction Grating Equation

  • A diffraction grating is a plate on which there is a very large number of parallel, identical, close-spaced slits
  • When monochromatic light is incident on a grating, a pattern of narrow bright fringes is produced on a screen

Diffraction grating diagram, downloadable AS & A Level Physics revision notes

Diagram of diffraction grating used to obtain a fringe pattern

  • The angles at which the maxima of intensity (constructive interference) are produced can be deduced by the diffraction grating equation

Grating equation, downloadable AS & A Level Physics revision notes

Diffraction grating equation for the angle of bright fringes

  • Exam questions sometime state the lines per m (or per mm, per nm etc.) on the grating which is represented by the symbol N
  • d can be calculated from N using the equation

Angular Separation

  • The angular separation of each maxima is calculated by rearranging the grating equation to make θ the subject
  • The angle θ is taken from the centre meaning the higher orders are at greater angles

Angular separation, downloadable AS & A Level Physics revision notes

Angular separation

  • The angular separation between two angles is found by subtracting the smaller angle from the larger one
  • The angular separation between the first and second maxima n1 and n2 is θ2 – θ1

Orders of Maxima

  • The maximum angle to see orders of maxima is when the beam is at right angles to the diffraction grating
    • This means θ = 90o and sin θ = 1

  • The highest order of maxima visible is therefore calculated by the equation:

  • Note that since n must be an integer, if the value is a decimal it must be rounded down
    • E.g If n is calculated as 2.7 then n = 2 is the highest order visible

Worked example

An experiment was set up to investigate light passing through a diffraction grating with a slit spacing of 1.7 µm. The fringe pattern was observed on a screen. The wavelength of the light is 550 nm.Worked Example: Diffraction Grating, downloadable AS & A Level Physics revision notesCalculate the angle α between the two second-order lines.

Worked example - diffraction grating equation (2), downloadable AS & A Level Physics revision notes

Exam Tip

Take care that the angle θ is the correct angle taken from the centre and not the angle taken between two orders of maxima.

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Lindsay Gilmour

Author: Lindsay Gilmour

Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.

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