2.20 Core Practical 6: Investigating Diffraction Gratings

Aim of the Experiment

• To find the wavelength of light using a diffraction grating

Variables

• Independent variable = Distance between maxima, h
• Dependent variable = The angle between the normal and each order, θ_n (where n = 1, 2, 3 etc)
• Control variables
  • Distance between the slits and the screen, D
  • Laser wavelength, λ
  • Slit separation, d

Equipment List

• Resolution of measuring equipment:
  • Metre ruler = 1 mm
  • Vernier Callipers = 0.01 mm

Method

The setup of apparatus required to measure the distance between maxima h at different angles θ

1. Place the laser on a retort stand with the diffraction grating in front of it
2. Use a set square to ensure the beam passes through the grating at normal incidence and meets the screen perpendicularly
3. Set the distance D between the grating and the screen to be 1.0 m using a metre ruler
4. Darken the room and turn on the laser
5. Identify the zero-order maximum (the central beam)
6. Measure the distance h to the nearest two first-order maxima (i.e. n = 1, n = 2) using a vernier calliper
7. Calculate the mean of these two values
8. Measure distance h for increasing orders
9. Repeat with a diffraction grating with a different number of slits per mm

• An example table might look like this:

Analysing the Results

The diffraction grating equation is given by:

nλ = d sin θ

• Where:
  • n = the order of the diffraction pattern
  • λ = the wavelength of the laser light (m)
  • d = the distance between the slits (m)
  • θ = the angle between the normal and the maxima (°)

• The distance between the slits is equal to:

• Where
  • N = the number of slits per metre (m^–1)

• Since the angle is not small, it must be calculated using trigonometry with the measurements for the distance between maxima, h, and the distance between the slits and the screen, D

• Calculate a mean θ value for each order
• Calculate a mean value for the wavelength of the laser light and compare the value with the accepted wavelength
  • This is usually 635 nm for a standard school red laser

Evaluating the Experiments

Systematic errors:

• Ensure the use of the set square to avoid parallax error in the measurement of the fringe width
• Using a grating with more lines per mm will result in greater values of h. This lowers its percentage uncertainty

Random errors:

• The fringe spacing can be subjective depending on its intensity on the screen, therefore, take multiple measurements of w and h (between 3-8) and find the average
• Use a Vernier scale to record distances w and h to reduce percentage uncertainty
• Reduce the uncertainty in w and h by measuring across all visible 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 clear

Safety Considerations

• Lasers should be Class 2 and have a maximum output of no more than 1 mW
• Do not allow laser beams to shine into anyone’s eyes
• Remove reflective surfaces from the room to ensure no laser light is reflected into anyone’s eyes