8/16/2019 Michelson Interferometer(Edited)

1/3

Michelson Interferometer - Graphical Summary

Amar Masalmeh∗ and Donald Ng Jer Yi†

Department of Physics, Simon Fraser University, Burnaby, BC, Canada 

(Dated: April 15, 2016)

∗ amasalme@sfu.ca† djng@sfu.ca

1

mailto:amasalme@sfu.camailto:djng@sfu.camailto:djng@sfu.camailto:amasalme@sfu.ca

8/16/2019 Michelson Interferometer(Edited)

2/3

I. INTRODUCTION

The Michelson Interferometer is a device used to study interference patterns in light

waves. This is done by splitting the incident light beam into two parts (reflected and

refracted) and recombining (using mirrors) into one beam. This process is known as ”in-

terferometric recombination” and illustrates the wave properties of light. The goal of this

experiment is to investigate some of these properties.

We have gathered data for the calculation of  K  (the ratio of micrometer to mirror move-

ment),  λNa  (the mean wavelength of Sodium), and ∆λ (the separation between the Sodium

Doublet).

We have also collected data for the calculation of  n (the refractive index of air) by creating

a vacuum in part of the path the light travels through.

II. METHOD

We first began by using a Mercury vapour lamp to observe circular fringes. Then, by

rotating the micrometer, the mirror would move, causing fringes to expand or contract.

These quantities would be related to one another with the following equation:

2∆d =  λ∆m   (1)

where λ  = 546.07 nm for green Mercury vapour light, ∆d is the mirror distance, and ∆m is

the number of passing fringes.

We then replaced the Mercury vapour lamp with a Sodium lamp. Using the same tech-

nique and equation as with the Mercury vapour lamp, we calculated the mean wavelength

of Sodium light,  λNa.

We then observed that Sodium fringes became indistinguishable after the mirror has been

moved a certain distance. This was due to the ”beating” signal between the two dominant

frequencies in Sodium’s emission spectrum. We measured the average carriage distance

required to move through one full contrast cycle. This was related to the separation between

Sodium’s dominant wavelengths by the following equation:

∆λ = λ1λ2

2∆d  (2)

2

8/16/2019 Michelson Interferometer(Edited)

3/3

where   λ1   and  λ2   are the two dominant wavelengths in the emission spectrum of Sodium.

The product  λ1λ2   is the square geometric mean of these two wavelengths, and can be ap-

proximated by   λ2

Na, the square arithmetic mean wavelength of Sodium light (mentioned

above).

Finally, we used a vacuum pump to evacuate a chamber (length 5 cm) of air. We expected

the optical path distance to change as pressure in the chamber changed. This minute change

was observed as fringe contractions of green Mercury light. The relevant quantities were

related by the following equation:

n = 1 +  mλp

2L∆ p  (3)

III. RESULTS

We calculated our K value to be 5.1 ± 0.36. More accuracy would have been beneficial

in reducing the errors in all our other calculations. Nonetheless, this value seemed accurate

enough for our purposes.

We found our  λNa  value to be equal to 588 ± 0.4  nm. This is very close to the accepted

value of  λNa  = 589.3  nm1.

We found our ∆λ value to be equal to 0.6± 0.05  nm. This is very close to the accepted

value of ∆λ = 0.60  nm1.

Lastly, we found our  n  value to be equal to 1.00029± 0.000006. This is extremely close

to the accepted value of  n = 1.0002922.

[1] Sodium Light Fringe Data -   http://physics.nist.gov/PhysRefData/Handbook/Tables/

sodiumtable2.htm.

[2] Sodium Light Fringe Data -   http://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_

7.html.

3

http://physics.nist.gov/PhysRefData/Handbook/Tables/sodiumtable2.htmhttp://physics.nist.gov/PhysRefData/Handbook/Tables/sodiumtable2.htmhttp://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_7.htmlhttp://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_7.htmlhttp://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_7.htmlhttp://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_7.htmlhttp://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_7.htmlhttp://physics.nist.gov/PhysRefData/Handbook/Tables/sodiumtable2.htmhttp://physics.nist.gov/PhysRefData/Handbook/Tables/sodiumtable2.htm