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Light - Determining the Wavelength of Light


                     

Theory: When coherent light shines through a diffraction grating, interference occurs. The wavelength of the light can be calculated using this formula dsinθ = nλ. Where lambda (λ) represents the wavelength of light, n is the order of the interference spot, d is the separation distance between the slits in the grating, and θ is the angle between the central maximum and the bright spot in question.

Variables

  • n is the order of the interference spot, where n=0 for the central maximum spot, ±1 for the first order maximum spot, ±2 for the second order maximum spot, etc.
  • d is the separation distance between the separate slits/grooves.  You will assume that the information printed on the slide is correct, in giving the number of grooves per millimeter.  Use this to find d.  Calculate the distance, d, between slits in meters.
  • θ is the angle between the central maximum and the bright spot in question.  Calculate the angle using trigonometry

Procedure:

  • Darken the room. (Caution: use a low-power laser, avoid contact with anyone's eyes.)
  • Shine a laser through the diffraction grating at flat screen of graph paper.
  • Photograph the diffraction (interference) pattern seen on the screen.

Calculations

  • Enter your diagram of diffraction, illustrating how wavelength is calculated in this DropBox folder.
  • Enter Data in this data table.
  • On either side of the central maximum is a dimmer spot known as first order maximum.  This is a location of constructive interference in which waves add.  Measure the distance between the central maximum and the first two maxima. (n=1, 2)
  • Determine the distance between the diffraction grating and the screen (Lx), and the distance between the central maximum and a first order maximum (Ly).
  • Calculate the angle (θ) between the central maximum and the first order maximum as the arctangent (tan-1) of the ratio of Ly / Lx
  • Calculate the wavelength (λ) of the laser light in meters.  dsinθ = nλ; λ =(dsinθ)/n
  • Calculate the wavelength of the red, green and blue lasers. Enter the values in the collaborative data table as requested.
  • What are the average of the calculated wavelengths for the red, green and blue lasers?

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