Physics Online
Diffraction
Introduction
Diffraction occurs when light waves interfere with each other. A diffraction grating consists of a thin
piece of opaque glass or plastic with a pattern of equally-spaced, transparent slits. If a beam of
monochromatic light (that is, light of only one wavelength) is incident on a diffraction grating at 90°,
then a series of bright and dark bands (called fringes) will emerge. The location of the bright bands is
given by the diffraction grating equation:
d*sinθ = mλ (m = 0, 1, 2,....).
The variable d is the distance between the centers of the grooves in the diffraction grating, θ is the
angle between the line connecting the center of the grating and the bright band and the line
perpendicular to the grating, m is called the order of the band and λ is the wavelength of the light.
Notice that the angle of diffraction depends on the wavelength. Red light (longer wavelength) is
diffracted through a larger angle than blue light (shorter wavelength). This means that a diffraction
grating can spread polychromatic light (that is, light of more than one wavelength) into its component
colors. A diffraction grating can also be used to determine the wavelength of monochromatic light,
such as that from a laser.
The mixture of wavelengths of light is called its spectrum. The spectrum is directly related to the
structure of the atoms and molecules that produced it. Therefore, spectral measurements are very
useful to scientists. A device capable of measuring the spectrum of a light source is called a
spectrometer. One way to make a spectrometer is by using a diffraction grating.
The purpose of this lab is to test the diffraction grating equation.
Equipment You Procure
 fluorescent or gas tubes (you don’t need to buy them, just find them)
 tape measure or meter stick
 tape
 an assistant
 a large, dark room
Equipment from Kits
x
 spectroscope
 diffraction grating
 laser (do not aim at anyone’s eyes)
θ
L
Experimental Procedures
Wavelength of a Laser
1) Solve the diffraction grating equation for λ, the wavelength of the light.
2) Calculate d, the distance between grooves (in meters) based on the labelled number of grooves per mm. If
the grating is not labelled, then assume 500 grooves per mm.
3) Use trigonometry to derive a formula for sinθ in terms of x and L. See the above figure. Substitute this
expression into the equation derived in step 1. Note that at no point in this lab do you need to calculate any
angles through inverse trig functions. If you do so, then you will lose points on your report.
4) Tape the diffraction grating to a horizontal surface so that the grating is vertical. The grating should be a
large distance from a wall and parallel to the wall.
5) Measure the distance between the diffraction grating and the wall, L.
6) Turn off the lights.
7) Aim the laser at the diffraction grating. You should notice an odd number of dots on the wall, typically 5.
The one in the center should be the brightest (m = 0).
8) Measure the distance between the center dot and one near it, x. This is a location for m = 1.
9) Calculate the wavelength of the light (use your formula from step 3) and compare it to the theoretical value
of 650 ± 10 nm.
10) Repeat steps 8 and 9 using a dot that is 2 dots away from the center. This will be m = 2.
11) Repeat steps 4 through 10 using a different location for the diffraction grating. This will give you a total of 4
calculations of the wavelength.
12) Optional: if you have access to a green laser, you can try calculating its wavelength in a similar manner.
Wavelength Limits of Polychromatic Light
13) Aim the spectroscope at light coming from outside. Do not aim your spectroscope at the sun! Note that the
scale on the spectroscope is in 100s of nm.
14) Record the wavelength of the upper limit (far edge of rusty red) of the continuous spectrum produced by
white light from an outdoor source.
15) Record the wavelength of the lower limit (far edge of deep purple) of the continuous spectrum produced
by white light.
16) Compare your results to the accepted values of approximately 400 and 700 nm. Note that the human vision
system can sense light with wavelengths of 312 nm and 1050 nm, but the sensitivity is 1/1000 that of the
normal range.1
Emission Spectra
1) Find a fluorescent or gas tube. Record its apparent color. Record the location of this tube if it is in a public
place.
2) Use your spectroscope and record the wavelength, color, width (sharp or fuzzy), and relative intensity
(bright or faint) for each line.
3) Compare your list of wavelengths, colors, widths, and relative intensities to the table below and attempt to
identify the element present.
4) If your list does not match that of one of the elements in the table below, then consult the following web
site: http://physics.nist.gov/PhysRefData/Handbook/atomic_number.htm (click on a suspected element,
then click on the link “strong lines” near the top of the page).
5) Repeat steps 1 through 4 with a different tube. At least one of the tubes must be outside your home. Get
out of your basement and head to a commercial area at night!
Element
Helium
Wavelength (nm) Color
Comment
388.9
Violet
Faint
447.1
Indigo
501.6
Green
587.6
Yellow-Orange
667.8
Red
706.5
Dark Red
Faint
Hydrogen
410.0
Violet
Faint
434.0
Indigo
486.1
Light Blue
656.3
Red
Krypton
427.4 to 484.7
Blue
Spread
557.0
Yellow-Green
587.0
Orange
Mercury
435.8
Indigo
546.1
Yellow-Green
567.5 to 580.3
Yellow
Neon is a case where the lines are so rich that it is more the
absence of certain colors rather than the presence of specific lines
that gives away its presence. This is in the range of 490 to 530 nm.
1 Hecht, Physics, 3rd edition, Thomson Brooks/Cole, 2003, pg. 800
2 Weast, CRC Handbook of Physics and Chemistry, 60th edition, CRC, 1980