# 3.5 The michelson interferometer  (Page 3/7)

 Page 3 / 7

## 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?

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

what is bohrs model for hydrogen atom
hi
Tr
Hello
Youte
Hi
Nwangwu-ike
hii
Alvin
what is the value of speed of light
1.79×10_¹⁹ km per hour
Swagatika
what r dwarf planet
what is energy
কাজের একক কী
Jasim
কাজের একক কী
Jasim
friction ka direction Kaise pata karte hai
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
b) symmetric of time only
Swagatika
fundamental note of a vibrating string
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
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
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
What is the importance of de-broglie's wavelength?
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
how do I differentiate this equation- A sinwt with respect to t
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
vy beautiful equation
chandrasekhar
what is electro statics
when you consider systems consisting of fixed charges
Sherly