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,?θn?(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 and 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

轉載自savemyexams