The Wave Nature of Light: Interference and Diffraction
Pre-Lab Question
UM Physics Demo Lab 07/2013
Light is said to behave as a wave and as a particle. Cite an example of each type of
behavior for light.
EXPLORATION: Diffraction
Materials
Red Level Laser
40 watt “candle” bulb on wooden base
Power strip
Diffraction grating (white border)
Unknown diffraction grating (colored border)
4 Medium binder clips (support legs for diffraction gratings)
2 Meter sticks
Calculator
Caution: The LASERs we will use today are safe for general use, but must
be handled with care. NEVER look into the LASER or shine it into someone’s
eye. ALWAYS TURN THE LASER OFF WHEN NOT IN USE and ONLY turn it on
when it is POINTED SAFELY AT THE WALL.
Lab Tip: Diffraction gratings degrade with finger oil and scratches. To
maintain top performance, please handle the diffraction gratings by their
edges and avoid touching the clear plastic portions of the gratings.
Monochromatic Light: The LASER
To demonstrate the wave nature of light and study interference effects, we need a
source of monochromatic light—light of a single wavelength. In the early 1960’s
physicists developed a new and powerful way to generate monochromatic light using
electron transitions between atomic energy levels as a light source. This technique
was named Light Amplification through the Stimulated Emission of Radiation—the
LASER. Since its invention, the LASER has become an indispensable tool for science
and industry. LASERs read the digital data from CDs and DVDs, transmit vast
amounts of information over fiber optics, cut industrial parts with amazing precision,
replace metal knives in a variety of surgeries (particularly eye surgery) scan the bar
codes on your groceries and serve as pointers for public speaking presentations. The
first LASERs employed a high-voltage electrical discharge in gases such as Helium
mixed with Neon. Subsequently, solid-state LASER diodes have been developed and
are currently used for most applications. For our experiments we will use LASER
diode that emits monochromatic red light at a wavelength of 650 nm (1 nm = 10-9
meters). Within the bright LASER light spot we can regard the light as plane waves
with a 650 nm wavelength. This is a good approximation to true plane waves (which
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are infinite in spatial extent) since the laser spot size is ~10,000 wavelengths in
diameter so that the wave fronts look infinite in all directions for objects ~10
wavelengths in size illuminated by the laser spot.
1. Light has both particle-like and wave-like characteristics. In the previous lab
we explored the classical ray tracing behavior of light, which illustrates the
particle-like behavior of light. Now we will demonstrate the wave behavior
of light
A) Place the standard diffraction grating (plain white border) one meter from the
wall on the lab bench. Place the LASER behind it on the table so that it shines
through the grating toward the wall. Turn on the LASER and observe the resulting
pattern of light on the wall. Sketch the resulting pattern of LASER light below.
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2. The splitting of the LASER light into several beams is caused by diffraction.
We can use this effect to measure the spacing between the parallel lines
etched onto the surface of the diffraction grating.
Figure 1: Fraunhoffer Diffraction of a LASER beam. The diffraction grating
lines are out of the page.
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The geometry of the right triangles shown in Figure 1 yields the Fraunhoffer
Diffraction Formula:


y
m  d 
 m  0,1,2,3...
2
2
 L  y 
where  = wavelength of the LASER light (650 nm) and d = line spacing of the
grating. The integer m is called the order of the maximum. We will make our
measurements with the first order maximum so
m=1.
A) Check that the diffraction grating is one meter from the wall and measure
the distance from the central beam to the first maximum of the diffracted
beam. Record your measurements (in meters) below:
L= 1 m
y = ____________(m)
L2  y 2  ___________(m)
d. Set m = 1 and calculate the spacing between
the grating lines d. Show your work below. For the wavelength of the LASER light use
λ = 650 nanometers (recall one nanometer = 1 nm = 1 billionth of a meter = 1 x 10-9
meters) and report your answer in nanometers.
B) Solve the diffraction equation for
d = Grating Spacing =________________________(nm)
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APPLICATION
Now that we have calibrated the spacing of the diffraction grating, we can use it to
study the light emitted by different objects. Using diffraction in this way is called
spectroscopy, the study of the spectrum of emitted or absorbed light.
1. The larger the wavelength of light compared to the spacing of the diffraction
grating, the larger the angle of diffraction. Given that red light has a longer
wavelength than blue light, predict which color will be diffracted to a larger
angle and therefore appear farthest from the lamp.
2. View the glowing filament of the candle lamp through diffraction grating and
label the order of the colors you observe along the schematic spectrum bar
below. Which color appears the farthest from the lamp. Was your prediction
for the order of red and blue made in (1) correct?
Colors: R=Red, O=Orange, Y=Yellow, G=Green, B=Blue, I=Indigo,
V=Violet
LAMP
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3. Now view one of the hydrogen discharge lamps through the diffraction grating
provided. The gratings are set ½ meter from the lamp.
A) Describe how the hydrogen spectrum is different from the spectrum of the
glowing filament. What features are present in the Hydrogen spectrum that is not
present in the filament spectrum?
B)
In the spectrum you should see a bright red line. This spectral line is called
the Hα line of the Balmer spectral series of Hydrogen. The line corresponds to
a transition of the Hydrogen electron from the third excited state of the
Hydrogen atom to the second excited state. Astronomers map the
distribution of hydrogen gas in the Galaxy by observing the intensity of this
line to determine both the presence and amount of hydrogen in ionized gas
clouds. The prominent greenish-blue line is called Hβ. You should also be
able to see a faint violet line (Hγ) and you may be able to see a very faint line
in the far violet (Hδ). Measure and record the position y of the Hα line on
both sides of the discharge tube and average the two values to produce
your final measured y value.
yLeft (m)
yRight (m)
yAverage (m)
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C) Now use the diffraction equation to calculate the wavelength of the Hα spectral
line. Use L=1/2 meter and m =1. Show your calculation below.
L= 1/2 m
y = ____________(m)
L2  y 2  ___________(m)
λH-α = Wavelength of Hα Spectral Line =_____________(nm)
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4. Thus far we have used the known spacing of the diffraction grating to
measure the wavelength of light. But recall that we measured the grating
spacing by using the known wavelength of LASER light to probe the size of
the grating lines. This illustrates one of the most powerful applications of
diffraction: to probe the structure of objects too small to observe directly—
crystals and molecules. To probe small structures with coherent light requires
light of a wavelength comparable to the size of the object. For crystals and
molecules this means using very small wavelengths which correspond to XRay radiation, which we can regard as very short wavelength light. X-Rays
are difficult to work with, but we can “scale up” the process by using larger
objects and visible LASER light as a surrogate for X-Rays.
We have observed that vertical parallel lines on the diffraction grating split the
LASER beam horizontally:
Figure 2: The relationship between grating lines and the diffracted Laser beam.
A) Predict what will happen to the diffraction pattern if you rotate the grating
so that the lines are horizontal.
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B) Test your prediction for part A by rotating the grating. Sketch the patterns
of LASER spots for both the vertical and horizontal grating.
C) Predict what pattern of laser spots you would observe if you had two
gratings, one vertical and one horizontal in front of the LASER beam. Sketch
your predicted pattern below.
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C) Test your prediction from (C). Ask your instructor to provide you with a
second diffraction grating. Was your predicted pattern for the two crossed
gratings correct?
D) Shine the LASER onto the wall and place the unknown diffraction grating (colored
border) in front of the beam. Sketch the resulting diffraction pattern below.
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E) Based on your observations for (A-C) sketch the pattern of lines that would
produce this pattern for the unknown grating.
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5. Below is probably the most important diffraction image ever taken. It was
made by Rosalind Franklin in 1952 by exposing purified strands of DNA to XRays.
Figure 3: Early X-ray diffraction pattern from B-DNA made by Rosalind Franklin in
1952.
Your instructor will project a diffraction image of a small unknown object
for you.
A) Sketch the projected diffraction pattern below.
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B) Compare your sketch of the projected image to the DNA diffraction image.
Label two features on your sketch that are similar to ones present in the DNA
image. Also label two features present in the DNA image that do not appear in
the projected image. Note that the DNA image is a photographic negative
where dark regions correspond to bright X-Ray light.
C) Your instructor will lead a class discussion where you will attempt to deduce
the structure of the unknown object producing the projected diffraction pattern.
After this discussion, predict what structure (shape) might produce the projected
image.
D) Now view the unknown object under the microscope. What shape is
producing the projected pattern? What does this imply about the internal
structure of the DNA molecule?
Everyday Applications of Diffraction







Bar code scanners
Laser pointers
Laser levels for carpentry
holography
Determining atomic structure of matter (using X-Rays, or shortwavelength light). The double helix structure of DNA was discovered this
way (by Rosalyn Franklin)
Spectroscopy (for example, for chemical analysis and Astronomical
observations of the composition of stars)
Measuring stresses and strains in transparent materials
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Challenge Work:
1. One of the fundamental precepts of Quantum Mechanics is that the energy of
light is quantized, that is, light carries energy in discreet packets called
quanta. This is part of the particle like behavior of light. When light
interacts with matter and gives up its energy, it behaves as a particle called
a photon with a discreet, exact energy proportional to its frequency. The
proportionality constant is call Plank’s constant and is measured
experimentally to be h = 4.14 ×10-15 eV-s. The electron-volt (eV) is a unit of
energy corresponding to the work done when one electron of charge moves
through a potential difference of one volt. Optical light typically carries
energies of a few electron volts, making eV a convenient unit.
Consider the following two equations:
I. E  hf
II. c  f 
Equation I states the energy E of a photon of light is proportional to the frequency of
the light (a wave property!) and that the proportionality constant is Plank’s constant
h. Equation II is the relationship between propagation speed, frequency and
wavelength for light as a traveling wave. Here we denote the wave speed as the
speed of light c = 3.0 ×108 m/s.
A) Solve Equation II for the frequency f in terms of the speed of light
wavelength λ. Show your calculation below.
c and the
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B) Now substitute your result from (A) into equation I and obtain an expression for
the energy of a photon of light in terms of the wavelength, speed of light and Plank’s
constant. Show your calculation below.
C) Calculate the energy in eV corresponding to your measured value of the
wavelength for the Hа spectral line of Hydrogen. Be sure to convert the wavelength
in nanometers to meters. Show your calculation below.
Hα Photon Energy =____________________(eV)
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Summary
1. Light exhibits both wave-like and particle-like behaviors.
2. The principle of linear superposition says that the amplitudes of two or
more waves arriving at a point in space add at every instant of time. This
gives rise to interference, where two or more arriving waves add up to
larger amplitude, smaller amplitude or zero.
3. Waves which encounter structures small compared to their wavelengths
undergo diffraction whereby they bend around corners or obstacles.
4. Light waves projected through a slit narrower than the wavelength will
interfere to produce a pattern of alternately light and dark fringes.
5. A diffraction grating consists of many narrow parallel slits and
disperses light into its component wavelengths (colors). Each wavelength of
light will diffract to a specific angle after passing through the grating.
6. A diffraction grating can be used to measure the wavelength of atomic
emission lines. This application of diffraction is called spectroscopy.
7. Conversely, the diffraction of a monochromatic (one color—one wavelength)
beam of LASER light can be used to measure the spacing of a diffraction
grating.
8. Diffraction of monochromatic light from a LASER or X-Ray source can be used
to infer the size and structure of small objects, crystals and molecules.
Small structures produce large diffraction angles; large structures
produce small diffraction angles.
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