• 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

Diagram of diffraction grating used to obtain a fringe patter

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

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

• 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 n_2?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

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 theh/D = tanθ

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