Name: Steven
K. Wonnell
Institution: Johns Hopkins University
Address: Physics and Astronomy Department
366
Bloomberg Center
3400
N. Charles Street
Baltimore,
MD 21218
Apparatus Title: Demonstrating the coherence length of
white light
Abstract (50-75 words)
The short
coherence length of white light is demonstrated by showing how the insertion of
a microscope slide over one of a pair of slits removes the two-slit
interference pattern. The coherence
length can be estimated by covering each slit with a separate cover glass, and
bending one glass away from its slit until the interference pattern disappears.
Description:
When light from a point source strikes
a double slit, each slit produces a single-slit diffraction pattern
superimposed on each another. When the
light is coherent, the two waves interfere and generate the Young double slit
pattern shown at the top of Fig. 1.
When the two light waves are not coherent, one observes the single slit
diffraction pattern shown at bottom in Fig. 1, which in reality consists of two
such patterns spaced so closely together as to be indistinguishable. You can easily observe this effect yourself
using the flashlight, double-slit pattern, and microscope slide described
below.
Figure
1. Top, photograph negative of the
2-slit interference pattern observed with the point source and the upper of the
two slits that are circled in Fig. 4.
Bottom, photograph made with an identical geometrical arrangement, but
with one slit covered with a microscope slide.
A Mini Maglite® flashlight
is used as our “point” white light source. Its filament is tiny and its head
can be unscrewed from the flashlight, leaving the bulb mostly naked; these
factors make it a quite sharp point light source. It is sufficiently bright to make this demo possible for
observation in a large lecture hall. For
use, stand the flashlight on end by sticking its end into the head of the
flashlight, as shown in Fig. 2.
Figure 2. The Mini Maglite, with its head removed and
its body, inverted, stuck back into its head.
It produces about a 270 degree unobstructed cone of light. The filament is 0.25 mm in diameter and 1.3
mm long.
For the double slit, either one of two
patterns of the Cornell Slitfilm Demonstrator shown circled in Fig. 3 is
convenient for this demonstration.
Alternatively, a perfectly adequate double slit can be easily
constructed by taping a piece of aluminum foil by its edges to a microscope
slide, and using a razor blade to make two parallel slits separated by about ½
millimeter. The two slits need to be
separated by a sufficient macroscopic distance such that one can cover one slit
with a microscope cover glass or slide without covering the other.
Figure
3. Schematic arragement of the slits on
the Cornell Slitfilm Demonstrator.
Either one of the two pairs of slits covered by the oval will work for
this demo.
To demonstrate the short coherence
length of white light, stand preferably at least a meter away from the Mini
Maglite, and look at the bulb through one of the two double slit patterns
identified in Fig. 3. You should see a
double-slit interference pattern like the top pattern of Fig. 1. Next, place a microscope slide such that it
covers only one slit, so that you observe the single-slit diffraction pattern
shown in Fig. 2. This requires a bit of
finesse. Covering one slit adds an
additional (1-n)*t/l
wavelengths of light to its path between the point light source and your eye,
relative to the number of wavelengths along the path that goes through the
uncovered slit. Here, n is the index of refraction of the
glass, l is the
wavelength of the light, and t is the
thickness of the glass. With n = 1.5, l » 550 nm,
and t » 1 mm, this is an additional » 880
wavelengths. Since the coherence length
of white light is much shorter than this, the waves are not coherent at your
retina and the interference pattern is not seen. Note that when you shift the microscope slide so that it covers
both slits, the two-slit interference pattern returns.
It is instructive to compare white
light with laser light. We take a laser
pointer, and put a short (18 mm) focal length lens in front of it to expand the
beam and reduce its intensity. When one
applies the same zero-, one-, then two-slits-covered technique just described
using the laser source, one notices that the two-slit interference pattern is
retained even when only one slit is covered.
This demonstrates that the coherence length of the laser light must be
longer than the amount (724 wavelengths for 670 nm laser light) retarded by the
microscope slide. In fact, typical laser light has a coherence length of many
hundreds of meters. Fig. 4 shows our
laser arrangement.
Fig. 4. Our laser pointer and lens arrangement. Tape is used to hold the laser’s switch in
the on position.
To estimate the coherence length of
white light, cover both slits with two microscope cover glasses, side by side,
such that each glass covers one slit.
Keep one glass flat and bend the other glass at an angle to the plane
containing the slits, all the while observing the light source. You will observe that the double-slit
interference pattern dissolves into a single-slit diffraction pattern near some
angle q. Figure 5 illustrates the geometry of this
situation.
Figure 5. Double-slit covered by two microscope cover
glasses, one bent at an angle to the double-slit film layer, with simplified
ray diagram. Not to scale.
From the geometry of Fig. 5 and Snell's
Law, the additional number DN of
wavelengths introduced by bending the cover glass by an angle q can be
shown to be
DN = !Unexpected End of Formula
which is plotted in Fig. 6, below, with
t = 0.16 mm (measured with a
micrometer), l = 550 nm,
and n = 1.5.
Figure
6. Plot of DN
as a function of the angle q shown in
Fig. 4.
Our observation is that the
interference pattern disappears when q is somewhere between 20 and 30
degrees. This corresponds to an upper
limit of 25 wavelengths or so for the coherence length, which is surprisingly
large compared to the accepted value of a few wavelengths.
Equipment:
|
Item |
Supplier |
catalog
no. |
price |
amount
in package |
amount
needed |
cost |
|
Mini Maglite |
REI |
410074 |
$10.00 |
1 |
1 |
$10.00 |
|
Slitfilm Slides |
CENCO |
WL3800A |
$132.00 |
10 |
1 |
$13.20 |
|
Fisherbrand Microscope Slides |
Fisher |
12-550A |
$26.72 |
144 |
1 |
$0.19 |
|
Fisherbrand Microscope Cover Glass 22x22-1 |
Fisher |
12-542B |
$14.59 |
about 100 |
2 |
$0.29 |
|
Scotch Tape |
Office Depot |
171553 |
$0.99 |
300” |
30” max |
$0.10 |
|
Laser Pointer |
Harbor Freight |
37431-1VGA |
$5.99 |
1 |
1 |
$5.99 |
|
Double Convex Lens, 18mm convex |
Pasco |
OS-9132 |
$27 |
1 |
1 |
$27.00 |
|
Total |
|
|
|
|
|
$56.77 |
Notes:
Two lab stands and clamps are needed to hold the laser pointer and the
lens. Costs may be reduced by
substituting a home-made double slit as described in the paper (cost: 50¢) instead of the commercial Slitfilm
slide. Bare Mini Maglite bulbs ($1.25/each) powered by an external DC power
supply can substitute for the flashlight.
Also, a regular-size Maglite will also work for this demo.
Acknowledgements:
The homemade double-slit idea comes
from Waves, by Frank S. Crawford, Jr.
(McGraw-Hill, 1968), pp.522. The idea
of using a Maglite comes from Doug Johnson of CSU-Pomona. Thanks go to Brad Frey whose request
inspired this demo.
It came to my attention during the
preparation of this submission that E. Hecht describes a demo similar to the
one described here in his Optics, 3rd ed., p. 556. However, the technique of bending the cover
plate, and our particular apparatus with its ease of use, are still original,
as far as I know!