<< Chapter < Page Chapter >> Page >

Summary

  • When the mirror in one arm of the interferometer moves a distance of λ / 2 each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe.

Key equations

Constructive interference Δ l = m λ , for m = 0, ±1, ±2, ±3…
Destructive interference Δ l = ( m + 1 2 ) λ , for m = 0, ±1, ±2, ±3…
Path length difference for waves from two slits to a common point on a screen Δ l = d sin θ
Constructive interference d sin θ = m λ , for m = 0 , ± 1 , ± 2 , ± 3 ,…
Destructive interference d sin θ = ( m + 1 2 ) λ , for m = 0, ± 1 , ± 2 , ± 3 ,
Distance from central maximum to the m th bright fringe y m = m λ D d
Displacement measured by a Michelson interferometer Δ d = m λ 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] .

Got questions? Get instant answers now!

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 μ m . How many fringes will cross the observing field?

Got questions? Get instant answers now!

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 × 10 −4 m

Got questions? Get instant answers now!

When the traveling mirror of a Michelson interferometer is moved 2.40 × 10 −5 m , 90 fringes pass by a point on the observation screen. What is the wavelength of the light used?

Got questions? Get instant answers now!

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 × 10 −6 m

Got questions? Get instant answers now!

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?

Picture shows a schematics of a set-up utilized to measure the refractive index of a gas. The glass chamber with a gas is placed in the Michelson interferometer between the half-silvered mirror M and mirror M1. The space inside the container is 5 cm wide.
Got questions? Get instant answers now!

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 ° and 0.86 °

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Red light ( λ = 710. nm ) illuminates double slits separated by a distance d = 0.150 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

Got questions? Get instant answers now!

Two sources as in phase and emit waves with λ = 0.42 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.

Got questions? Get instant answers now!

Two slits 4.0 × 10 −6 m apart are illuminated by light of wavelength 600 nm. What is the highest order fringe in the interference pattern?

6

Got questions? Get instant answers now!

Questions & Answers

what is bohrs model for hydrogen atom
Swagatika Reply
hi
Tr
Hello
Youte
Hi
Nwangwu-ike
hii
Alvin
what is the value of speed of light
Propessor Reply
1.79×10_¹⁹ km per hour
Swagatika
what r dwarf planet
Sivalakshmi Reply
what is energy
Isiguzo Reply
কাজের একক কী
Jasim
কাজের একক কী
Jasim
friction ka direction Kaise pata karte hai
Rahul Reply
friction is always in the opposite of the direction of moving object
Punia
A twin paradox in the special theory of relativity arises due to.....? a) asymmetric of time only b) symmetric of time only c) only time
Varia Reply
b) symmetric of time only
Swagatika
fundamental note of a vibrating string
fasoyin Reply
every matter made up of particles and particles are also subdivided which are themselves subdivided and so on ,and the basic and smallest smallest smallest division is energy which vibrates to become particles and thats why particles have wave nature
Alvin
what are matter waves? Give some examples
mallam Reply
according to de Broglie any matter particles by attaining the higher velocity as compared to light'ill show the wave nature and equation of wave will applicable on it but in practical life people see it is impossible however it is practicaly true and possible while looking at the earth matter at far
Manikant
a centeral part of theory of quantum mechanics example:just like a beam of light or a water wave
Swagatika
Mathematical expression of principle of relativity
Nasir Reply
given that the velocity v of wave depends on the tension f in the spring, it's length 'I' and it's mass 'm'. derive using dimension the equation of the wave
obia Reply
What is the importance of de-broglie's wavelength?
Mukulika Reply
he related wave to matter
Zahid
at subatomic level wave and matter are associated. this refering to mass energy equivalence
Zahid
it is key of quantum
Manikant
how those weight effect a stable motion at equilibrium
Nonso Reply
how do I differentiate this equation- A sinwt with respect to t
Evans Reply
just use the chain rule : let u =wt , the dy/dt = dy/du × du/dt : wA × cos(wt)
Jerry
I see my message got garbled , anyway use the chain rule with u= wt , etc...
Jerry
de broglie wave equation
LoNE Reply
vy beautiful equation
chandrasekhar
what is electro statics
fitsum Reply
when you consider systems consisting of fixed charges
Sherly
Practice Key Terms 1

Get the best University physics vol... course in your pocket!





Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 3' conversation and receive update notifications?

Ask