CIE AS Physics (9702) 2019-2021

Revision Notes

9.2.5 The Diffraction Grating

The 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

 

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
  • 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

Worked example

Worked example - diffraction grating equation (1), downloadable AS & A Level Physics revision notes
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.

Determining the Wavelength of Light

Method

  • The wavelength of light can be determined by rearranging the grating equation to make the wavelength λ the subject
  • The value of θ, the angle to the specific order of maximum measured from the centre, can be calculated through trigonometry
  • The distance from the grating to the screen is marked as D
  • The distance between the centre and the order of maxima (e.g. n = 2 in the diagram) on the screen is labelled as h – the fringe spacing
  • Measure both these values with a ruler
  • This makes a right-angled triangle with the angle θ as the ratio of the h/D = tanθ

Wavelength of light setup, downloadable AS & A Level Physics revision notes

The wavelength of light is calculated by the angle to the order of maximum

 

  • Remember to find the inverse of tan to find θ = tan-1(h/D)
  • This value of θ can then be substituted back into the diffraction grating equation to find the value of the wavelength (with the corresponding order n)

Improving experiment and reducing uncertainties

  • The fringe spacing can be subjective depending on its intensity on the screen. Take multiple measurements of h (between 3-8) and finding the average
  • Use a Vernier scale to record h, in order to reduce percentage uncertainty
  • Reduce the uncertainty in h by measuring across all fringes and dividing by the number of fringes
  • Increase the grating to screen distance D to increase the fringe separation (although this may decrease the intensity of light reaching the screen)
  • Conduct the experiment in a darkened room, so the fringes are clearer
  • Use grating with more lines per mm, so values of h are greater to lower percentage uncertainty

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