Name:_________________________________________________________________
Lab Section: ___________
Lab Partners: ___________________________________________________________ Grade:____________
Physics 202
Experiment #7
Diffraction Grating
Pre-Lab
Introduction
In this experiment you will be using a spectrometer and a diffraction grating to measure the various
wavelengths of the spectral lines of mercury vapor.
A diffraction grating is a multiple-slit device which produces spectral lines that are very sharp and
widely spaced. Gratings can be made by ruling a large number of fine lines on a carefully prepared
piece of glass or metal with a diamond point. In the case of glass, the transparent openings between the
opaque lines constitute the parallel slit system. A grating will produce constructive interference for
different wavelengths of light at an angle  m to the incident beam of light. The equation relating this
diffraction angle to the wavelength and slit separation of the grating is
m  d sin m , m  1, 2,3,...
(1)
where  is the wavelength of the diffracted light, d is the grating space (distance between adjacent
lines), and m is the order of diffraction. That is, m = 1 for the first order diffraction, m = 2 for the
second order diffraction, and so on.
Pre-lab Questions (turn in at start of lab)
1. Some of the gratings used in lab have 300 lines/mm etched on them. Find the distance, d, between
the lines for such a grating.
2. Using the largest and smallest wavelengths in the table in the lab (on page 4), calculate the firstorder angle for each, and calculate the angle between them (this is the width of your spectrum).
Assume the grating described in #1.
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3. Suppose you look at the spectrum produced by the grating described in #1, then look at the
spectrum produced by a second grating. You find that all the colors are diffracted to larger angles
by this second grating. Are the lines on the second grating closer together or farther apart?
4. Does the second grating have more or fewer than 300 lines/mm?
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Name:_________________________________________________________________ Lab Section: ___________
Lab Partners: ___________________________________________________________ Grade:____________
Physics 202
Experiment #7
Diffraction Grating
Introduction
In this experiment you will be using a spectrometer and a diffraction grating to measure the various
wavelengths of the spectral lines of mercury vapor. A spectrometer is an instrument for producing and
viewing the various lines (or wavelengths) of the spectrum. As shown in Figure 1, it consists of a
collimator C to produce a parallel beam of light, a diffraction grating G mounted on its table to
disperse the light into its spectrum, and a telescope T with which to examine the spectrum.
Figure 1. Diffraction grating; telescope positions.
You have already used the spectrometer to find speed of light as a function of wavelength by
dispersing the spectral lines of mercury through a prism. Your familiarity with the apparatus will help
you make accurate measurements of the wavelengths for this experiment.
A diffraction grating is a multiple-slit device which produces spectral lines that are very sharp and
widely spaced. Gratings can be made by ruling a large number of fine lines on a carefully prepared
piece of glass or metal with a diamond point. In the case of glass, the transparent openings between the
opaque lines constitute the parallel slit system. A grating will produce constructive interference for
different wavelengths of light at an angle  m to the incident beam of light. The equation relating this
diffraction angle to the wavelength and slit separation of the grating is
m  d sin m , m  1, 2,3,...
(1)
where  is the wavelength of the diffracted light, d is the grating space (distance between adjacent
lines), and m is the order of diffraction. That is, m = 1 for the first order diffraction, m = 2 for the
second order diffraction, and so on. The number of lines per inch or per mm, N, should be printed on
your grating.
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Part I. Measurement of Wavelength
Turn on the mercury lamp. The collimator has been adjusted so that the light coming through the slit
comes out as parallel rays. The grating has also been adjusted so that its plane is perpendicular to the
incident rays. Be careful not to move the grating table. If you do, don’t touch anything else and realign it by using the accepted value for wavelength for one of the spectral lines in the table below and
the expected diffraction angle. You can do this by setting the telescope arm on the expected diffraction
angle and rotating the table until the spectral line lines up with the cross hairs. To double-check that
the grating is indeed perpendicular to the incoming beam, swing the telescope to the other side of the
grating and make sure you obtain the same reading of angle for the same spectral line on this side.
Using the spectrometer and equation (1), find the value of wavelength for six different spectral
lines. Similar to the previous lab where you calculated the index of refraction using the spectrometer,
use the Verniers to make measurements of the diffraction angle of spectral lines to the nearest minute
of arc. Compare your values of the wavelengths with the accepted values given below and calculate the
percent error.
Also in each case determine the experimental error in the wavelength. Careful when propagating error
with angles! If you have an expression that multiplies something by , such as C  sin   , that 
had better be in radians. Any time you mess around with angles outside of a trig function, use radians!
The data for this part of the experiment consists solely of a table. Be sure to include all relevant
information and label it clearly.
Wavelength (nm) Color
404.7
407.8
435.8
491.6
496.0
546.1
577.0
579.1
615.2
623.2
violet
violet
blue
blue-green
blue-green
green
yellow
yellow
orange-red
orange-red
Part II. Finding an Unknown Grating Spacing
Switch out the gratings in your table, being careful not to change alignment. If you do, be sure to
realign the grating by using one of the known spectral lines and the procedure above.
1) Just from noticing the trend in spectral lines, (did they spread further apart, or get closer
together?) and not taking an actual reading of angle, do you expect the grating lines of the
unknown grating to be closer or further apart than what you used in Part I? Explain.
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Measure the diffraction angles for the same spectral lines you calculated in Part I with this new grating.
Using your values of wavelength from Part I and your values of diffraction angles from Part II make a
plot of this data in whatever way you want to extract the value of the unknown grating spacing, d.
2) What did you choose to plot for the x- and y-axes and why?
3) Does your data from the plot confirm your qualitative analysis in question 1?
4) If your “unknown” grating actually has the spacing written on it, what is the percent error in your
measured value?
Post-lab Questions:
1. The wavelength of a given spectral line can be determined most accurately by making observations
on the image of highest order. Why? Prove this by using your equation for error in wavelength and
common sense. Assume that there is no error in m. However, what is a drawback experimentally
about using higher order lines?
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2. What was the objective of this lab? Do you feel the objective was appropriately achieved? Why or
why not?
3. Name the two most significant sources of scientific error in this experiment (Be specific – do NOT
say, for example, “human error” or “equipment limitations”). Are these errors likely to be random
or systematic? Explain.
4. Describe some ways that the error in this lab could be reduced, including the possible purchase of
additional equipment. (Continue on the next page if necessary.)
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