Interference Flashcards
What is the optical path (phase delay) in material of index n?
2πnL/π
What is the free space propagation phase delay
2πL/π
What is the phase difference between free space and material n
2π(n-1)L/π
Why can we not directly measure phase delays
light waves oscillate much too fast for any instrument
What indirect method is used to measure phase delays
interferometers
how are interferometers used to measure phase delays
by mapping the phase onto light intensity which can be directly measured
What is constructive interference
- coherent
- waves combine in phase to give a high irradiance
What is destructive interference?
- coherent
- waves combine 180 degrees out of phase and cancel out yielding zero interference
What is incoherent addition
waves combine with lots of different phases to give a very low irradiance
where on the waves do we compute phase delay
from one wavefront to another potential wavefront because phase is constant along wavefronts
How will the phase delay look if the scattering is constructive and coherent
the same (mod 2π)
how will the phase delay look is the scattering is destructive and coherent
uniformly varying from 0 to 2π
under what condition will a beam remain a plane wave
if there is a direction for which coherent constructive interference occurs
For relflected beams what are the conditiions for constructive and destructive interference
incident angle must equal reflected angle for constructive
if an angle is too big, symmetry disappears and the phases are all different
What is an interference fringe
where beams have overlapped in space and time
(in words) How is the crossing angle of beams related to the fringe spacing?
large crossing angle => closely spaced fringes
What is the fringe spacing formula?
Ξ = 2π/2π sin π = π/2 sin π
What happens to the intensity pattern at a crossing angle of zero?
It becomes constant
What is the minimum visible fringe spacing?
0.1mm
What is intensity of interference
I(phase delay) = I0(1+mcos(phase delay))
where I0 = sum of squared amplitudes of interfering waves
what is the formula for the visibility of fringes
π = (πΌπππ₯ β πΌπππ)/(πΌπππ₯ + πΌπππ)
where I max = sum of amplitudes squared and I min is difference of amplitudes squares
How to you ensure high contrast/fringe visibility
By interfering beams of equal amplitudes
What are the interferometers based on 2 beam interference
Michelson and Mach-Zehnder
If the michelson mirros are exactly perpendicular, what will they produce
circular fringes
what is the formula for the phase difference in a michelson interferometer
πΏ = 2π* 2(πΏ1 β πΏ2)/π
When can white light fringes be observed in the michelson interferometer
when L1=L2 exactly
What happens when you tilt the mirrors of the Michelson Interferometer
- vertical fringes appear in the field of view
- moving the second mirror by half a wavelength moves each fringe by the fringe spacing difference
If m fringes cross a line when M2 moves a distance d in the Michelson Interferometer, what is the wavelength
d= mπ/2 or π=2d/m
What is the role of the beam splitter on the michelson interferometer
- reflection occurs off the front surface
- transmitted beam passes through the beam splitter 3 times
- reflected beam passes through once
What is the role of the compensator plate in the michelson interferometer
- it is identical to the beam splitter to equalise the path length through glass
How can we vary the phase delay for a michelson interferometer
introduce a gas cell into one of the paths with refractive index delta n
What is the additional phase change for a michelson interferometer with a gas cell
phase change = 2π*2(deltan-1)tcell/π
What happens when we misalign the mirrors of the michelson interferometer
the beams cross at an angle when they recombine at the beam splitter
What is the intensity for crossed beams if the input to the michelson interferometer is a plane wave
I=I1+I2+Re{E0 exp[i(wt - kzcosπ-kxsinπ]E0*[-i(wt-kzcosπ+kxsinπ]}
What does crossing beams do?
Maps delay onto position
What happens when we change the path length of one arm in the michelson interferometer?
we introduce a 2kd phase shift so the fringes will shift by 2kd
Describe the unbalanced Michelson Interferometer
- An object is placed in one arm
- so in addition to the spatial factor, one beam will have a spatially varying phase
- the fringes will be distorted in position
- phase variations of a small fraction of a wavelength can be measured
what is the cross term for an unbalanced michelson interferometer
Re{exp[2iphase(x,y) exp[-2ikxsinπ]}
How is the Mach-Zehnder Interferometer usually operated
- 2 beam splitters and 2 mirrors in a rectangle
- misaligned with something of interest placed in one arm
- due to the open geometry, this object can have a large volume
What is a common use of the M-Z
to observe density variations in gas-flow patterns within wind tunnels, shock tubes and plasma chambers
