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

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Rotating grating (as in Ebert or Czerny-Turner mounting), shown above.

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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 90º, 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 90º. 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!

Download spreadsheet in
Excel format (.xls)
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 90º, 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 90º. 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!

Download spreadsheet in OpenOffice format (.ods)

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:

**Grat1**is a stationary grating with incident white light, pictured above. Eight colors of diffracted light shown in the first order only, plus the zeroth order reflection shown as a gray line. The colors of the diffracted beams roughly match the wavelengths of those beams. Students can change the angle of the incident beam and the grating ruling density. Download links: Grat1.WKZ. This model is also available in OpenOffice format (.ods) and in Excel format (.xls).**Grat2**is a stationary grating with incident white light, used to demonstrate the relationship between the first and second orders of diffraction. Six visible colors of diffracted light shown in the first and second orders, plus the zeroth order reflection shown as a gray line. The colors of the diffracted beams roughly match the wavelengths of those beams. Students can change the angle of the incident beam and the grating ruling density. Download link: grat2.wkz**Grating**is a stationary grating with monochromatic incident light. Diffraction in the zeroth, first, and second orders are shown. The diffracted beams are shown in shades or gray and patterns; no use of color is made. Students can change the angle of incidence, the wavelength of the incident light beam, and the grating ruling density. Download link: Grating.wkz.**CzernyTurner**is a rotating grating in a Czerny-Turner mounting. Diffraction in the zeroth, first, and second orders are shown. The diffracted beams are shown in shades or gray and patterns; no use of color is made. Students can change the angle of rotation of the grating, the angle between the incident beam and observed diffracted beans, the wavelength of the incident light beam, and the grating ruling density. Download link: CzernyTurner.wkz.

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.

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: