index previous next

Animated Diffraction grating

Microsoft Excel and OpenOffice Calc Versions


Fixed grating. Download Excel or Calc version.

Rotating grating. Download Excel or Calc version.
            

Animated model of a plane diffraction grating, with sliders to control the angle of incidence, the ruling density, and the diffraction order viewed. Based on the grating equation: Angle of diffraction = asin(order*wavelength /(groove spacing) - sin(angle of incidence)). 

Assumptions: The grating surface is represented by the striped bar on the left of the figure. It is illuminated with a thin parallel, collimated "white" light beam consisting of eight discrete wavelengths. Only one diffraction order is shown at a time (selected by the number wheel). Only eight wavelengths are shown in the diffracted beam. The colors of the diffracted beams roughly match the wavelengths of those beams. The relative intensity of different wavelengths and orders is not represented.  For clarity, narrow beams are shown, even though in practical applications a wide beam, entirely covering the grating surface, is ordinarily used. Angles are measured from the horizontal axis.

View Equations (.pdf)

Fixed grating with variable angle of incidence
Download spreadsheet in Excel format (.xls)
Download spreadsheet in OpenOffice format (.ods)

Rotating grating (as in Ebert or Czerny-Turner mounting), shown above.
Download spreadsheet in Excel format (.xls)
Download spreadsheet in OpenOffice format (.ods)

There is also an alternative version with 4 different pairs of wavelengths separated by 1 nm, useful for demonstrating the conditions leading to the highest dispersion.  The angular dispersion of a grating is determined by differentiating the diffraction angle with respect to wavelength and is equal to order*(ruling density) /cos(angle of diffraction), where the ruling density is the number of grating lines per unit length.  As the angle of diffraction approaches 90, its cosine approaches zero, and the angular dispersion approaches infinity.  So the dispersion is expected to be greatest for whatever wavelength is diffracted close to 90. Of course, you can't actually use a diffraction angle of 90 degrees, but you should be able to get close.  If you achieve a sufficiently high angular resolution, you'll be able to separate the diffracted beams into two close-spaced wavelengths. Try it!  

../SimpleModels/DiffractionGrating3.GIF

Download spreadsheet in Excel format (.xls)
Download spreadsheet in OpenOffice format (.ods)

Wingz Version

WingZ version
          Grat1.wkz
WingZ version Grat1.wkz
[OpenOffice and Excel Versions]

Four "Animated figure" models that help students understand diffraction gratings in stationary and Czerny-Turner mountings. There are four variations of this model:

These models can be operated using only the mouse-activitated on-screen sliders and radio buttons, useful when used in a lecture-demonstration environment with a computer video projection system, in a darkened room, where it is difficult to use the keyboard data entry .

Wingz player application and basic set of simulation modules, for windows PCs or Macintosh

There is also a set of diffraction grating models written in Matlab. See below for Excel and OpenOffice Calc versions.

[Return to Index]

Mathematical basis

Inputs:
(All angles measured from the perpendicular to the grating surface.)
Angle of incidence = alpha, degrees, changed by typing into entry table or by slider
Ruling density = R, lines/mm, changed by typing into entry table or by radio buttons

Calculated quantities:
Groove spacing = d, 1000000/R (displayed in nm in table).
alphar = alpha/(360/(2*pi()))
Angle of diffraction = asin(order*wavelength/d-sin(alphar))



Revised June 2009. (c) 1991, 2009, Prof. Tom O'Haver , Professor Emeritus, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at toh@umd.edu. Number of unique visits since May 17, 2008: