Measuring Wavelength With Diffraction Grating

Determining the Wavelength of Light

Equipment Listing

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

Young's Double-Slit Experiment

The overall aim of this experiment is to investigate the human relationship between the distance between the slits and the screen, D, and the fringe width, w

• Contained variable = Fringe width, westward
• Dependent variable = Distance between the slits and the screen, D
• Control variables
  • Laser wavelength, λ
  • Slit separation, s

Method

The setup of appliance required to measure the fringe width w for different values of D

1. Set up the apparatus by fixing the laser and the slits to a antiphon stand up and place the screen so that D is 0.v m, measured using the metre ruler
2. Darken the room and plough on the light amplification by stimulated emission of radiation
3. Measure out from the fundamental fringe beyond many fringes using the vernier callipers and dissever past the number of fringe widths to observe the fringe width, w
4. Increase the distance D by 0.ane m and repeat the procedure, increasing it by 0.one chiliad each time up to around 1.5 thou
5. Echo the experiment twice more and calculate and record the mean fringe width westward for each distance D

• An case tabular array might wait like this:

Analysing the Results

• The fringe spacing equation is given past:

• Where:
  • due west = the distance between each fringe (m)
  • λ = the wavelength of the laser light (m)
  • D = the altitude between the slit and the screen (thou)
  • due south = the slit separation (m)

• Comparing this to the equation of a straight line: y = mx
  • y = w (m)
  • x = D (k)
  • Gradient = λ / s (unitless)

• Plot a graph of w against D and draw a line of best fit
• The wavelength of the light amplification by stimulated emission of radiation light is equal to the slope multiplied by the slit separation

λ = slope × s

Interference by a Diffraction Grating

The overall aim of this experiment is to calculate the wavelength of the laser calorie-free using a diffraction grating

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

Method

The setup of apparatus required to mensurate the altitude between maxima h at different angles θ

1. Place the laser on a antiphon stand and the diffraction grating in front of it
2. Utilise a ready square to ensure the beam passes through the grating at normal incidence and meets the screen perpendicularly
3. Ready the distance D between the grating and the screen to be one.0 m using a metre ruler
4. Darken the room and turn on the laser
5. Place the zero-club maximum (the central axle)
6. Measure the distance h to the nearest 2 first-gild maxima (i.e. northward = 1, due north = 2) using a vernier calliper
7. Calculate the mean of these ii values
8. Measure distance h for increasing orders
9. Repeat with a diffraction grating with a different number of slits per mm

• An case tabular array might look like this:

Analysing the Results

The diffraction grating equation is given by:

nλ = d sin θ

• Where:
  • northward = 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 betwixt the slits is equal to:

• Where
  • North = the number of slits per metre (m^–i)
• Since the angle is not small, it must be calculated using trigonometry with the measurements for the distance betwixt maxima, h, and the distance betwixt the slits and the screen, D

• Calculate a mean θ value for each order
• Summate 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 gear up square to avert parallax error in the measurement of the fringe width
• Using a grating with more lines per mm volition effect in greater values of h. This lowers its percentage uncertainty

Random errors:

• The fringe spacing can exist subjective depending on its intensity on the screen, therefore, take multiple measurements of westward and h (between 3-eight) and notice the average
• Utilize a Vernier calibration to record distances w and h to reduce pct dubiousness
• 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 subtract the intensity of light reaching the screen)
• Behave the experiment in a darkened room, so the fringes are clear

Safe Considerations

• Lasers should exist 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 light amplification by stimulated emission of radiation low-cal is reflected into anyone'southward eyes

Worked Example

A student investigates the interference patterns produced past two unlike diffraction gratings. One grating used was marked 100 slits / mm, the other was marked 300 slits / mm. The altitude between the grating and the screen is measured to be 3.75 grand.The student recorded the distance between adjacent maxima afterward passing a monochromatic light amplification by stimulated emission of radiation source through each grating. These results are shown in the tables below. Calculate the mean wavelength of the laser light and compare it with the accepted value of 635 nm. Assess the percentage uncertainty in this effect.

Measuring Wavelength With Diffraction Grating,

Source: https://www.savemyexams.co.uk/as/physics/ocr/18/revision-notes/4-electrons-waves--photons/4-9-superposition--stationary-waves/4-9-6-determining-the-wavelength-of-light/

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