5.11.5 Transmission Diffraction Grating

• Dispersion is the separation of visible white light into a spectrum of its colours
  • This can be done using a glass prism or a diffraction grating
• Transmission diffraction gratings are useful for separating light of different wavelengths with high resolution in order to:
  • Analyse light from stars
  • Analyse the composition of a star

Diffraction gratings are most commonly used in spectrometers to analyse light from stars

• A transmission diffraction grating is a glass or plastic slide containing a large number of regularly spaced, parallel slits or lines
• It is used to analyse spectral line wavelengths from the light emitted by stars
  • The angular dispersion (separation) of the colours is much greater using a transmission diffraction grating than an optical prism
  • Using diffraction gratings results in sharper fringes compared to using a double slit

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

• 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

• 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 = 90^o 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