SPEED OF LIGHT
We use a Helium Neon LASER (wavelength 632.8nm), photodiode detector, and fast
digital oscilloscope to directly measure the change in time taken for light to reach the
detector as the detector is moved some distance (displacement over time). In order to do
this we use pulses of light that are naturally produced by the LASER. The pulses are
produced with a frequency that depends on the length of the laser cavity. For the most
current laser we are using this pulse spacing is roughly 2.0-3.0ns. The use of these
naturally occurring laser beats makes the lab very simple, and is the most significant
property of the current method (you should investigate what is happening). This is a
unique method of measuring the speed of light and requires specific laser properties.
The optics is set up to split light (using a 50-50 beam splitter) and send light to two fast
amplified silicon photodiode detectors. When light hits these detectors a small current is
produced. Since the pulse has a very narrow time width the cables must be terminated at
50ohms. A larger resistance would smear the pulse out in time and make it not visible on
an oscilloscope. This resistance gives a small RC time constant and Voltage=IR (Ohm's
law). The voltage is small due to the small current and small resistance. Thus there is
relatively little signal (compared to using a 1.0MegaOhm termination) even though there
is lots of light. The oscilloscope records voltage vs. time. The voltage is proportional to
the intensity of incident light. It is important to note that the photodiodes are quite
sensitive to position within the laser beam. You will need to find a position such that the
detector is not saturated.
1.
LASER AND CABLES
Remove jewelry, watches, rings, etc. from hands (no reflecting surfaces in laser
beam). Place these somewhere safe where you will find them when you are
finished. Use either 2.00m sticks or a long tape measure to measure signal
detector positions along the tables. Set the detector near the end by the laser.
Turn laser on. Be careful of this laser beam. Do not stare into “direct” reflections
off the lens or other surfaces. Connect the trigger cable to the oscilloscope
channel two (being careful not to disrupt the trigger detector position). You may
need to align the trigger detector to get good triggering signal. The trigger signals
the oscilloscope to start data acquisition (start the stopwatch). Once the trigger is
set it must not be disrupted for the remainder of your experiment (this affects the
timing). Connect the signal cable to channel one. As you move the signal
detector the pulse peaks will move on the oscilloscope screen (take longer to
reach detector). DISCONNECT THE CABLES LATER WHEN YOU ARE
FINISHED. You must move the signal detector in small increments (compared to
what) in order to track the motion of a spe4cific peak relative to the trigger.
2.
TURN ON SCOPE—power in the lower left. Make sure the run/stop button is
green (running). The channel 1 and channel 2 buttons may be turned on or off at
your convenience. You will want to first look at channel 2 to set up triggering.
When you press the ch. 1 or 2 button the menu settings will display for that
channel.
Some typical settings for both channels are:
Ch. 1—50 Ohm (signal)
Ch. 2—50 Ohm (trigger)
DC—both channels
BW full
Scale approx. 50 mV/division (from 2.0 to 100 may be typical)
Time Scale 2.00ns/division (This gives 20.0ns across the screen and is what you want --why)
Find the “Acquire” button, press it and make sure the mod you are in is:
Average
512
Record length 100k
Now turn Channel 1 off so that you display only channel 2 and run through your
triggering setup by selecting the trigger menu button.
Edge
Source 2
Slope up
Mode normal
Adjust the trigger level until good signal (NOTE YOU MAY HAVE TO ADJUST THE
DETECTOR POSITION).
ONCE YOU HAVE GOOD TRIGGERING—DO NOT ADJUST THE LASER OR THE
TRIGGER DETECTOR POSITION.
Note the “trig’d” indicator on the upper right of the screen.
3.
You are triggering. Switch channel 2 off, and turn channel 1 on.
You may need to adjust the signal detector left/right or up/down (this may need
correcting each time you move the detector).
Your signal detector should start close to the laser, and move back in increments
of less than 30.0 cm. You may use a mirror or two to send the laser back along
the table and continue taking data over a longer distance.
4.
Cursors
Hit the cursor button (while viewing good channel 1 signal).
You will have two cursors, a and b. For now set both on top of one another at a
peak as far to the left edge of the screen as possible and make sure you record the
time for cursor a. That is your starting time. If your signal is fluctuating too
much you may use the run/stop button to freeze the display.
5.
To take data:
You will move the detector position carefully measuring how far it has moved
from the initial starting point (total distance from start). Then you will observe
that the peak position has moved slightly on the oscilloscope screen. You should
move cursor “b” to the nearest new peak position just to the right of the initial
(not moving cursor a). Note and record position of the detector and also the time
for cursor b. Continue moving the detector, further is better (why). Make sure
none of your change in position increments is greater than 30 cm (why). Make
sure you record appropriate significant figures, all necessary scope settings, and
all necessary room or other conditions.
Prior to leaving the room and completing your data acquisition you should use
your endpoint data to do a quick check on your results. You should have a result
within a couple percent of the accepted value.
While taking data you should carefully consider uncertainty in determining
positions and times.
6.
You may want to take pictures of setup to include in your final draft lab report.
You should also copy the following onto a flash drive (the scope has usb). You
will copy a sample data set of voltage vs time data onto a file on your flash drive
(waveform not image---note the difference). You will import your data into a
program of your choice and make a plot of the waveform. SAVE THE DATA
FILE NOT IMAGE. IF YOU ARE NOT SURE THEN DO BOTH.
7.
Discussion and Analysis.—General tasks
You have data of position vs. time for a pulse of light reaching a detector at some
position and some time after it reached a trigger. You will need to calculate the
speed of light in air.
a)
First use your "endpoints" (first and last point) data to get a rough value for the
speed of light. This will be in your lab book at the time you take the data (if it
does not look good you need to redo data). You know the answer.
Generate a rough approximation of your uncertainty by just considering the
endpoint data and how well you know the times and positions. Be fair about
estimating those uncertainties. Think about how well you can measure the
position and also the time for the peak.
Later when you plot and fit a best line to your data you will receive an uncertainty
in your result (ORIGIN IS RECOMMENDED) which is determined only by the
statistical spread in your data. Your lab report will use the statistical spread (but
this should agree well with your estimated rough uncertainty and you should say
so in your lab report).
Work on your data analysis, include your plot with fitted line, include uncertainty
from linefit and also from experiment, include your graph of the sample data set.
Your report must give the results for speed of light in air along with its
uncertainty. You should also include a comparison with the standard value.
There are many factors that are unique to our method that you should consider
(this is your place to be creative and unique). –above and beyond minimums!!!!!!
You will need to show me that you can make some quick measurements and
calculations to give the speed of light. You will have lab books available. This is
open ended (expect me to investigate the limits of your knowledge).
b)
c)
d)
e)
f)
g)