# 3.5 The michelson interferometer  (Page 3/7)

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## Summary

• When the mirror in one arm of the interferometer moves a distance of $\lambda \text{/}2$ each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe.

## Key equations

 Constructive interference $\text{Δ}l=m\lambda ,\phantom{\rule{0.6em}{0ex}}$ for m = 0, ±1, ±2, ±3… Destructive interference $\text{Δ}l=\left(m+\frac{1}{2}\right)\lambda ,\phantom{\rule{0.2em}{0ex}}\text{}\phantom{\rule{0.2em}{0ex}}$ for m = 0, ±1, ±2, ±3… Path length difference for waves from two slits to a common point on a screen $\text{Δ}l=d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta$ Constructive interference $d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =m\lambda ,\phantom{\rule{0.6em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}m=0,\text{±}1,\text{±}2,\text{±}3\text{,…}$ Destructive interference $d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =\left(m+\frac{1}{2}\right)\lambda ,\phantom{\rule{0.2em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}m\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}0,\text{±}1\text{,}\phantom{\rule{0.2em}{0ex}}\text{±}2\text{,}\phantom{\rule{0.2em}{0ex}}\text{±}3\text{,}\dots$ Distance from central maximum to the m th bright fringe ${y}_{m}=\frac{m\lambda D}{d}$ Displacement measured by a Michelson interferometer $\text{Δ}d=m\frac{{\lambda }_{0}}{2}$

## Conceptual questions

Describe how a Michelson interferometer can be used to measure the index of refraction of a gas (including air).

In one arm, place a transparent chamber to be filled with the gas. See [link] .

## Problems

A Michelson interferometer has two equal arms. A mercury light of wavelength 546 nm is used for the interferometer and stable fringes are found. One of the arms is moved by $1.5\mu \text{m}$ . How many fringes will cross the observing field?

What is the distance moved by the traveling mirror of a Michelson interferometer that corresponds to 1500 fringes passing by a point of the observation screen? Assume that the interferometer is illuminated with a 606 nm spectral line of krypton-86.

$4.55\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\phantom{\rule{0.2em}{0ex}}\text{m}$

When the traveling mirror of a Michelson interferometer is moved $2.40\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}\text{m}$ , 90 fringes pass by a point on the observation screen. What is the wavelength of the light used?

In a Michelson interferometer, light of wavelength 632.8 nm from a He-Ne laser is used. When one of the mirrors is moved by a distance D , 8 fringes move past the field of view. What is the value of the distance D ?

$D=2.53\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}\text{m}$

A chamber 5.0 cm long with flat, parallel windows at the ends is placed in one arm of a Michelson interferometer (see below). The light used has a wavelength of 500 nm in a vacuum. While all the air is being pumped out of the chamber, 29 fringes pass by a point on the observation screen. What is the refractive index of the air? ## Additional problems

For 600-nm wavelength light and a slit separation of 0.12 mm, what are the angular positions of the first and third maxima in the double slit interference pattern?

$0.29\text{°}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}0.86\text{°}$

If the light source in the preceding problem is changed, the angular position of the third maximum is found to be $0.57\text{°}$ . What is the wavelength of light being used now?

Red light ( $\lambda =710.\phantom{\rule{0.2em}{0ex}}\text{nm}$ ) illuminates double slits separated by a distance $d=0.150\phantom{\rule{0.2em}{0ex}}\text{mm}.$ The screen and the slits are 3.00 m apart. (a) Find the distance on the screen between the central maximum and the third maximum. (b) What is the distance between the second and the fourth maxima?

a. 4.26 cm; b. 2.84 cm

Two sources as in phase and emit waves with $\lambda =0.42\phantom{\rule{0.2em}{0ex}}\text{m}$ . Determine whether constructive or destructive interference occurs at points whose distances from the two sources are (a) 0.84 and 0.42 m, (b) 0.21 and 0.42 m, (c) 1.26 and 0.42 m, (d) 1.87 and 1.45 m, (e) 0.63 and 0.84 m and (f) 1.47 and 1.26 m.

Two slits $4.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}\text{m}$ apart are illuminated by light of wavelength 600 nm. What is the highest order fringe in the interference pattern?

6

#### Questions & Answers

what is an atom
Aroyameh Reply
All matter is composed of two sets of three dimensions. The first set (1,2,3) decay with a positive charge. The second set (4,5,6) decay with a negative charge. As they decay, they create space (7 8,9) dimensions.
John
Two sets of (1,2,3,4,5,6) dimensions create a proton, a neutron, and an electron. This is the primordial atom.
John
A 10kg mass lift to a height of 24m and release. what is the total energy of the system
ADEPOJU Reply
mechanics is that branch of physical and mathatics that
ADEPOJU
E=Mgh=10*10*24=2400J
Adamu
what is the difference between a molecule and atom
Natanim Reply
Atoms are single neutral particles. Molecules are neutral particles made of two or more atoms bonded together.
Manfred
what I'd dynamic propulsion
Elias Reply
A body quadruples its momentum when its speed doubles.What was the initial speed in units of c.i.e..what was u/c ?
Lekshmi Reply
what is enthalpy?
prabir Reply
a thermodynamic quantity equivalent to the total heat content of a system
RAMLA
proparty of tharmo dainamic
bloch
What is the meaning of Nuclear Fission?
Benita Reply
what do you mean by dynamics single particles
Peacekamei Reply
عند قذف جسم إلى أعلى بسرعة إبتدائية فإنه سيصل إلى ارتفاع معين (أقصى ارتفاع) ثم يعود هابطاً نحو سطح الأرض .   إذا قُذِفَ جسم إلى أعلى ووجد أن سرعته 18 م / ث عندما قطع 1/4 المسافة التي تمثل أقصى ارتفاع سيصله فالمطلوب إيجاد السرعة التي قُذِف بها بالمتر / ث . إن هذه السرعة هي واحدة من الإجابات التالية
Aml Reply
what is light
Ayebanifesunday Reply
light is a kind of radiation That stimulates sight brightness a source of illumination.
kenneth
Electromagnet radiation creates space 7th, 8th, and 9th dimensions at the rate of c.
John
That is the reason that the speed of light is constant.
John
This creation of new space is "Dark Energy".
John
The first two sets of three dimensions, 1 through 6, are "Dark Matter".
John
As matter decays into luminous matter, a proton, a neutron, and an electron creat deuterium.
John
There are three sets of three protons, 9.
John
There are three sets of three neutrons, 9.
John
A free neutron decays into a proton, an electron, and a neutrino.
John
There are three sets of five neutrinoes, 15.
John
Neutrinoes are two dimensional.
John
A positron is composed of the first three dimensions.
John
An electron is composed of the second three dimensions.
John
What is photoelectric
Hsssan Reply
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
Michael
i.e. Solar pannel.
Michael
Photoelectric emission is the emission of electrons on a metal surface due to incident rays reflected on it
Benita
If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
Rakhi Reply
it has everything to do with the angle the UV sunlight strikes your sunglasses.
Jallal
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
Jallal
I hope I'm clear if I'm not please tell me to clarify further or rephrase
Jallal
what is bohrs model for hydrogen atom
Swagatika Reply
hi
Tr
Hello
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Hi
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hi
Siddiquee
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Omar
helo
Mcjoi
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Propessor Reply
1.79×10_¹⁹ km per hour
Swagatika
3×10^8
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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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