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
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
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!
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
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.
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 .
(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
Groove spacing = d, 1000000/R (displayed in nm in table).
alphar = alpha/(360/(2*pi()))
Angle of diffraction = asin(order*wavelength/d-sin(alphar)) (c) 1991, 2015. This page is part of Interactive
Computer Models for Analytical Chemistry Instruction, created
and maintained by 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 firstname.lastname@example.org.
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