• 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 pattern

• 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

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
• 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

Worked example

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

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