Physics 318-L

Laboratory Report

Speed of Light

Laboratory No.1

Written by: Eric Krage Lab Section 01

Lab Partner: Sarah, Haaken, Alan Date Performed: 1/23/12

Instructor: Dr. McTaggart

Abstract:

The objective of this lab was to determine the speed light in fiber optic cable and in air. For the speed in the cable a comprehensive fiber optic apparatus was used. The speed of light in fiber optic wire was 2.98x10^8 m/s. For in air a modulated laser was split into two beams that were connected to a device that connected to an oscilloscope to measure the offset of the two peaks produced. The speed of light in air was determined to be 5.29x10^8 m/s.

Apparatus

Comprehensive Fiber Optic Apparatus, Oscilloscope, modulated laser, fiber optic wire, black circuitry control box, beam splitter, mirror, and lenses.

Fig 1. Comprehensive Fiber Optic Apparatus and setup.

Fig 2. Setup for speed of light in air

A. We included a lens that focused the beam reflected back from the mirror.

Procedure

The initial step was to become familiar with the laboratory manual and locate all the apparatus needed. Using figure 1 to set up the fiber optic cable to the transmitter and receiver, the oscilloscopes’ differential probes where attached across the transmitter and receiver to measure the time delay. From this measurement a delay can be measured in the transmission and reception which will allow for calculating the speed of light as well as the index of refractions of the cable. Part B involves measuring the speed of light in air, setup figure 2 the distance had to be shortened to allow for placement in the laboratory. The modulated laser needs to be hooked up to the oscilloscope along with the lines coming from the photodiode box. The laboratory was shortened to allow for 45 meters total. From this the time delay can be

measured from the laser pulse refracted off the mirror and the other off the lens. The difference can be obtained by using the cursor on the oscilloscope.

Data

Table 1. Comprehensive Fiber Optic Apparatus Data.

Fiber Optic

Index of refraction 1.665

L 20m± .05Time 110ns ±10ns

c 3.02727e8 ms±0.03

Table 2. Speed of light in air data

In Airtotal distance 42±0.5

time 120e-9s ±20ns

c 3.48e8ms±0.3

The reason for the error in Table 2 is due to the use of the lenses which when analyzed will slow down the laser beam for every centimeter of lens it traverses.

Error Propagation

Lets assumeQ=Q ( x )1is any function of x thenδQ=|dqdx|δx2

Assuming we take measurements of X and Y and some function F defines these variables, we can do a Taylor series expansion about the most probable values of X and Y such that we can have the first order approximation of the series.

f ( X ,Y )≅ f (X ,Y )+ ∂ f∂ X

¿X, Y+∂ f∂Y

¿X ,Y=f (X ,Y )+ ∂∂ X

f (X ,Y )+ ∂∂Y

f (X ,Y )3

The error in the function can then be represented as the following.

u {f }=√( ∂ f∂ X )2

(u {X } )2+( ∂ f∂Y )2

(u {Y } )24

whereu {f }=√ ∑α=X ,Y , Z…..

( ∂ f∂α )2

(u {α } )25

Example: Let A=Aoe-t/RC .6

∂ A∂ Ao

=e−t /RC= AAo, ∂ A∂t

=Ao (e−t /RC ) (−1RC )=−ARC

7

Now plugging into the uncertainty formula and getting the error in terms of A we have

( u {A }A )=√(u {A }

Ao )2

+( u {t }RC )

28

Sample Calculations

Part A . c=n∗Lt.9

n=index of refraction , L=lenght of wire ,∧t=time.

Example

c=3.027e8ms

=nLt

=1.665 (20m )110ns

. c=∆d∆t

.∆d was the distance¿ the laser ¿ themirror×2−distanceof beam splitter ¿circuitry box .

∆ t was thetime shift differnce observed onthe oscilloscope .

Example , c=3.48e8ms

=42m−0.7m120ns

=∆d∆ t

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Result Analysis

The results for Part A were close to the speed of light in a vacuum so our results are accepted. Part B shows more error than observed when using the other apparatus. This error could be due to the distance being too short, which will make the delay smaller that the oscilloscope might not pick up. Also some error could be contributed to the delay the laser observed when traveling through the lenses and being reflected by the mirror. One thing that improved our accuracy is the testing the delay and set up in as small of scale as possible to make calibration easier.

Conclusion

This laboratory procedure was straight forward and provided overall concise results. Both parts of the lab had their own challenges but once these where understood we could compensate for them. The answers where comparable to the desired value of the speed of light in a vacuum, to improve upon these measurements could be made by having an oscilloscope with a higher sampling rate. This would give a more precision answer, as well as more experience with that particular oscilloscope would also improve upon the operator error.

References

1. An introduction to Error Analysis, John R. Taylor. 2nd Edition

Images of set up