Experiment 6: Interferometers
Nate Saffold [email protected]
Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216
INTRO TO EXPERIMENTAL PHYS-LAB 1493/1494/2699 NOTE: No labs and no lecture next week! Outline
● The physics behind:
● EM waves
● EM in medium: reflection and refraction ● Interferometry:
● Fabry-Perot interferometer
● The experiment:
● Introducing the apparati
● Determine the wavelength of He-Ne laser separately for each interferometer.
● Measure the index of refraction of air and glass.
PHYS 1493/1494/2699: Exp. 6 – Interferometers 3 Electromagnetic waves
● Electromagnetic wave = oscillating electric and magnetic fields
● An EM wave propagates in vacuum at the speed of light
● Electric and magnetic fields are always perpendicular to each other
(James Clerk Maxwell… Pretty smart guy…) PHYS 1493/1494/2699: Exp. 5 – Polarization and Interference 4 Interference
● An essential property of waves is the ability to get combined with other waves
● The result of this superposition can lead to a wave with greater or smaller amplitude
● This phenomenon is called interference
Maxima superimposed Maxima superimposed to minima to maxima
They cancel out They add to each other
PHYS 1493/1494/2699: Exp. 5 – Polarization and Interference 5 EM waves and interference
● In this lab we will study the wave properties of light and in particular interference
● EM waves can superimpose in a constructive or destructive way
Constructive 1 ` = m + 2 Destructive✓ ◆
PHYS 1493/1494/2699: Exp. 6 – Interferometers 6 EM waves and interference
● As a result, when two different EM waves are superimposed they will some times overlap constructively, some times destructively and most often something in between
● The typical interference pattern therefore looks like:
Constructive
Something in between
Destructive
PHYS 1493/1494/2699: Exp. 6 – Interferometers 7 EM in medium
● Electric and magnetic fields in medium are different from those in vacuum
● Microscopic explanation: a dielectric material (insulator) can be polarized and hence change its own charge distribution. This changes the EM fields within the medium itself
● Macroscopic description: one defines an electric displacement field: Relative permittivity Electric displacement
For the most common dielectric Polarizability materials electric displacement is Susceptibility of proportional to applied electric field the medium PHYS 1493/1494/2699: Exp. 6 – Interferometers 8 EM in medium
● In general, electromagnetism in a medium is different from that in a vacuum
● Maxwell’s equations are different: They look pretty similar to me!
PHYS 1493/1494/2699: Exp. 6 – Interferometers 9 Refraction
● Question: if the behavior of EM waves is different from vacuum to medium, what does this cause?
● Refraction: bending of light when passing from a medium to another (e.g. vacuum to air, air to glass, etc.)
PHYS 1493/1494/2699: Exp. 6 – Interferometers 10 Refraction
● The behavior of light rays at an interface between two materials is described by the Snell’s Law:
PHYS 1493/1494/2699: Exp. 6 – Interferometers 11 Optical path length
● Question: what actually is an index of refraction?
● Since Maxwell’s equations are different the speed of light in a medium is different!
with: c = speed of light in vacuum v = speed of light in medium
● Consequence: EM waves originating from the same source but traveling in different media (i.e. different indices of refraction) over the same physical distance, have different optical path lengths.
PHYS 1493/1494/2699: Exp. 6 – Interferometers 12 Optical path length (OPL)
EM wave traveling in vacuum
EM wave traveling in a medium
● Two ways to change OPL =
● Change physical distance (obviously)
● Change index of refraction (i.e. put it in a different medium).
PHYS 1493/1494/2699: Exp. 6 – Interferometers 13 OPL in different mediums
● To study interference we only care about the phase difference between waves (i.e. the number of extra wavelengths that a wave travels)
● Let’s consider two waves traveling in two boxes of side L but filled with two different media (n1 and n2):
● The number of wavelengths contained in each box will be:
● Consequently, the number of extra wavelengths is:
Number of extra wavelengths Difference in index of refraction between two paths PHYS 1493/1494/2699: Exp. 6 – Interferometers 14 Interferometry
● Interferometry uses the interference of two rays generated from the same coherent source but having different path lengths
● The main idea is: 1. Start with the same coherent source (same , polarization, phase ) 2. Direct the two beams through different paths with path length difference equal to 3. Allow the beams to meet up again at some future point
● The two waves can now make constructive or destructive interference depending if: (Constructive interference)
(Destructive interference)
PHYS 1493/1494/2699: Exp. 6 – Interferometers 15 Michelson Interferometer
● Michelson (1881): invented it to measure the speed of the earth relative to the “ether”… and he didn’t find anything… sad story…
Albert, there is no ether… Told you…
● Idea: 1. Split single beam into two, then recombine. 2. Observer sees interference patterns projected onto a small screen. 3. By moving one of the mirrors, the observer can change the path length difference . The consequence is a shift in the interference pattern.
PHYS 1493/1494/2699: Exp. 6 – Interferometers 16 Michelson Interferometer
Viewing screen
Interference pattern appears here Beam splitter
Movable LASER mirror M1
Common coherent source OPL for beam 1 OPL for beam 2
Fixed mirror M2
PHYS 1493/1494/2699: Exp. 6 – Interferometers 17 Michelson Interferometer (on steroids…)
● Michelson interferometers can be pretty large…
LIGO @ Hanford Site, Washington VIRGO @ Cascina, Italy Cost ~ 620 million dollars Cost ~ 100 million euros Length ~ 4 km Length ~ 3 km ● These guys are so precise that can be used to detected minuscule space-time variations due to gravitational waves
PHYS 1493/1494/2699: Exp. 6 – Interferometers 18 Michelson Interferometer (on steroids…)
● As you probably heard from the news the LIGO interferometer was a huge success!
● On September 14th, 2015 at 09:50:45 UTC they recorded the very first signal coming from a gravitational wave going through the Earth
● This signal most likely came from two black holes with ~30 solar masses each merging together 1.3 billions years ago!
● Quite remarkable for ‘just’ an interferometer…
PHYS 1493/1494/2699: Exp. 6 – Interferometers 19 Fabry-Perot Interferometer
● Same idea: split beam and then recombine.
● However, instead of splitting the beam just once, it splits many times using mirrored cavity.
● Each reflection adds a small difference in path length,
● The final result is a circular interference pattern
● Main advantage: the fringes are brighter and well distinguishable
PHYS 1493/1494/2699: Exp. 6 – Interferometers 20 Condition for bright spots (constructive)
● The condition for the presence of bright spots is the same for both the previous interferometers
● Suppose we start with the two beams in phase and look at the position of a bright spot, then: 1. Modify one of the two path lengths bright spots will not be bright spots anymore 2. They will be bright spots again when the total path length difference is λ 3. This will happen again at 2λ, 3λ, etc.
● In general, if we change one of the paths by dm, in order to have a bright spot back in its original position we must have:
PHYS 1493/1494/2699: Exp. 6 – Interferometers 21 The Experiment
PHYS 1493/1494/2699: Exp. 6 – Interferometers 22 Goals
● In this experiment you will use both the Michelson and the Fabry-Perot interferometers
● Fabry-Perot Interferometer:
● Measure the wavelength of the He-Ne laser ● Michelson Interferometer:
● Measure the wavelength of the He-Ne laser
● Measure the index of refraction of air (nair).
● Measure the index of refraction of glass (nglass).
PHYS 1493/1494/2699: Exp. 6 – Interferometers 23 Fabry-Perot (FP) interferometer: setup
Move this guy = change in Adjustable Movable Converging lens mirror path length = change mirror interference pattern
Viewing Screen Circular fringes appear here LASER
Micrometer knob
Allows you to move the mirror by very small fractions of a mm PHYS 1493/1494/2699: Exp. 6 – Interferometers 24 How to read a micrometer
● The micrometer will allow you to move one of the two mirrors by very small distance. ● This will shift the interference patter
Example: In the Each of these picture you can marks is 1 µm read the 500 µm mark, the 25 µm mark and the knob reads 7 µm.
Position = 532 µm Each of these marks is 100 µm
PHYS 1493/1494/2699: Exp. 6 – Interferometers 25 FP interferometer: procedure
● Follow directions for FP setup on the lab manual
● A few tips:
● Turning the micrometer knob to move mirrors will cause the fringe pattern to change.
● Fringes move really fast! Do this with the help of a lab partner.
● Measure at least the passing of 20 fringes. The more fringes you measure, the better the measurement!
● Record distance dm that mirror moves and number of fringes passing through a fixed point.
● Repeat measurement 10 times for different dm! PHYS 1493/1494/2699: Exp. 6 – Interferometers 26 FP interferometer: He-Ne wavelength
● Plot dm vs. m (number of fringes):
● For each measurement, extract wavelength λ using above equation.
● Report average:
● Compare to accepted value of 632.8 nm
PHYS 1493/1494/2699: Exp. 6 – Interferometers 27 Michelson interferometer: setup
Viewing screen
LASER
Movable mirror Beam splitter
Lens
Adjustable mirror
PHYS 1493/1494/2699: Exp. 6 – Interferometers 28 Michelson interferometer: procedure
● Remove lens in front of the laser.
● Follow procedures as in lab manual.
● Tips for setup:
● For best results, make sure the two beams are almost exactly on top of each other before placing lens in front of laser!
● Same tips as in FP apply to Michelson. ● Measurement of He-Ne laser wavelength:
● Same procedure: Measure fringes vs distance of movable mirror. Take 10 trials.
● Report
● Compare to accepted value and Fabry-Perot Interferometer.
PHYS 1493/1494/2699: Exp. 6 – Interferometers 29 Michelson interferometer: measure nair
● Change the optical path length of the beam by changing the pressure:
● A change in pressure causes a change in index of refraction. ● Note: The change in pressure ΔP is linearly proportional to the change in index of refraction Δn.
● The schematic setup for the Michelson interferometer is going to be: Change in pressure = change in index of refraction = different wavelength
PHYS 1493/1494/2699: Exp. 6 – Interferometers 30 Vacuum cell and pump
Pressure gauge
Release toggle
Vacuum hand pump Vacuum cell mounted on rotational pointer
PHYS 1493/1494/2699: Exp. 6 – Interferometers 31 Michelson interferometer: measure nair
● The vacuum cell will be at Patm initially.
● You will slowly pump out the air to change the pressure and count the number fringes that pass through a certain point
● Pressure gauge reads cm Hg (not inches Hg)
● Unit conversion not important since we'll be only needing pressure differences (as long as you are consistent).
PHYS 1493/1494/2699: Exp. 6 – Interferometers 32 Calculating the index of refraction
● We already saw that the number of fringes passing a point when the index of refraction is changed is given by:
● Problem: neither ni nor nf are known.
● Solution: divide everything by the change in pressure:
● However: Δn/ΔP = α = constant
● Therefore: Linear relation between number of fringes passing through a point (m) and change in pressure
PHYS 1493/1494/2699: Exp. 6 – Interferometers 33 Michelson interferometer: Compute nair
● Make at least 7 measurements of m and ΔP
● Convert m to Δn through:
● Note: Use λ0 = 632.8 nm
● Plot ΔP vs. Δn:
● Determine slope α
● Now use Patm = 76 cm Hg, Pvac = 0, nvac = 1 to compute nair:
PHYS 1493/1494/2699: Exp. 6 – Interferometers 34 Measuring the index of refraction of glass
LASER
Glass mounted on rotational pointer
PHYS 1493/1494/2699: Exp. 6 – Interferometers 35 Measuring the index of refraction of glass
● Similar principle as nair: change in OPT = change in pattern
● Due to the angle of the glass with respect to the axis of the laser, the beam will refract according to Snell's Law:
● The incidence angle θ is related to the distance the beam travels inside the glass. (point A to point B)
● Rotating the glass (i.e. changing θ) will change the distance A to B that the beam travels and hence the pattern PHYS 1493/1494/2699: Exp. 6 – Interferometers 36 Measuring the index of refraction of glass
● Applying Snell's Law and doing a little geometry we get the following expression for nglass:
● Start marker at zero, then rotate to some angle θ and count the number of fringe shifts.
● Use equation above for nglass,
● Take 5 more measurements for various angles.
● Take average and report:
PHYS 1493/1494/2699: Exp. 6 – Interferometers 37 Tips
● Here are some (maybe) useful tips:
1. You will notice that the first fringe from the center is usually really thick while from the third on their are really thin. The best fringe to point for your counting is usually the second one 2. Setup is an essential part of the experiment. Do that as carefully as possible 3. Both the interferometers are really precise and they particularly suffer from vibration of the environment. Try to minimize them, for example, by not touching the table when performing a measure 4. The largest source of error is mostly likely mis-counting the number of fringes so assign a reasonably large error 5. When taking different data, always start counting from zero. This will avoid propagating mis-counted fringes 6. When using the micrometer is better to start measuring with respect to the 500 µm mark (linear response). Don’t forget to restart every time from there!
PHYS 1493/1494/2699: Exp. 6 – Interferometers 38 Summary
● Using the Michelson and Fabry-Perot interferometer and changing the optical path length of the beam, we can hopefully measure many parameters from our system.
● Wavelength of He-Ne laser
● Index of refraction of air and glass. ● This can be be the most difficult and tedious experiment all semester: Need to show up prepared to lab!!!
● That being said, it has a large potential for high quality data and a clear analysis.
PHYS W1493/W1494/W2699: Exp. 6 – Interferometers 39