phy 351, lab 2, formal report

8/16/2019 Phy 351, Lab 2, Formal Report

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P Y 351: Modern Physics

Lab 2: Measuring The Speed of Light

Group members:

Introduction

In this experiment, we employ a modern rendition of a method used by Foucault in 1862 to

measure the speed of light in air. We send a beam of laser so that it bounces back and forth

between a rotating mirror and a fixed mirror. Due to the rotation of one of the mirrors, the

flight path of the laser beam will vary slightly between the two times of arrival. This small

rotation will deflect the laser beam through a small angle, which produces a measurable effect.

The amount by which the laser beam deflects is directly proportional to the angular speed of

the rotating mirror. Therefore, at very high angular speeds (~2000 rad/s), we are able to use

a microscope to accurately determine the deflection of the beam.



Equipment

High-speed rotating mirror assembly

Measuring microscope

He-Ne Laser

Laser Alignment and Optics Bench

Lenses: Focal Length- 48mm and 252mm

Calibrated Polarizers

Fixed Mirror

Figure 1: Diagram of the Foucault Method

Experiment Procedures:

The apparatus is aligned and the beam is brought to sharp focus into the fixed mirror.

The pertinent distances are measured: distance between lens 2 and the rotating mirror(B),distance between rotating mirror and fixed mirror(D), distance between lens 2 and laser

source(A).

The angular speed of the rotating mirror is adjusted and the beam deflection is observed

through the microscope.

Deflection distances are measure using the micrometer for both clockwise and anti-clockwise

rotations.



Fig 2: Measurement Labels

Measurements

D = 3.9m

B= 0.416m

A= 0.3152m

Angular speed of Mirror, = = 2000 /

Deflection of beam:

Δ 10− Δ 10−)10.325 10.405

10.398 10.29

10.29 10.205

9.335 9.242

Calculations

The following equation is used to calculate the speed of light:

= 4 Δ′ / 1

After adjusting to fit the measured parameters, the equation becomes,



= 4 scw sccw / 2

Trial# Speed of Light, 10 /

1 2.6622

2 2.6710

3 2.6962

4 2.9746

Uncertainties

The percentage uncertainty in the speed of light is given by,

Δ = ±

+ Δ

+ Δ

ω+ Δ

+ Δ ( + +

) Δ 3

Substituting A = 0.3152 , B = 0.416 , D = 3.9 and = 2000 , we obtain:

Δ = ±8.8∗10 Δ 2.7585 ∗ 10Δ6.43∗10Δ7.79∗10Δ

Finally, we substitute the uncertainties in the meter rule and micrometer screw gauge,

Δ = ± 5 ∗ 1 0− , Δ = Δ = Δ = ±5 ∗ 10−

which gives the following uncertainty in our calculation of the speed of light,

Δ= ±1.423∗10

Therefore the percentage uncertainty is,

% = 4.75

Note that, for our calculation of the uncertainty in the speed of light, we have used the average

deflection value (s’).

Sources of experimental errors

The most significant source of error consists of the measurement of the deflection distance of the laser

beam. Since we have chosen a distance separation of 3.9m between the fixed and rotating mirrors, the



accuracy of the measured deflection value is likely to be lower. The greater the distance separation

between the mirrors, the more accurate the results.

Results & Conclusion

Our dataset contains four distinct trial attempts to measure the speed of light. The first three trials

yielded values that were in the range of ~2.66 2.69 ∗ 10 / .

The final trial, however, yielded the value of 2.9746∗10 / for the speed of light.

Note that the accepted value for the speed of light is: c = 2.99792458∗10 / .

This indicates that the values that we have experimentally obtained are in good agreement with the

exact value for the speed of light. If we consider the value calculated during the fourth trial, the

percentage error is merely,

% =

∗ 1 0 0 =2.997924582.9746

2.99792458 ∗100=0.778%

Hence, we can conclude that the results of this experiment are accurate and reliable.

phy 351, lab 2, formal report

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