Interference

Question 1

What is the optical path (phase delay) in material of index n?

Answer 1

2𝜋nL/𝜆

Question 2

What is the free space propagation phase delay

Answer 2

2𝜋L/𝜆

Question 3

What is the phase difference between free space and material n

Answer 3

2𝜋(n-1)L/𝜆

Question 4

Why can we not directly measure phase delays

Answer 4

light waves oscillate much too fast for any instrument

Question 5

What indirect method is used to measure phase delays

Answer 5

interferometers

Question 6

how are interferometers used to measure phase delays

Answer 6

by mapping the phase onto light intensity which can be directly measured

Question 7

What is constructive interference

Answer 7

• coherent
• waves combine in phase to give a high irradiance

Question 8

What is destructive interference?

Answer 8

• coherent
• waves combine 180 degrees out of phase and cancel out yielding zero interference

Question 9

What is incoherent addition

Answer 9

waves combine with lots of different phases to give a very low irradiance

Question 10

where on the waves do we compute phase delay

Answer 10

from one wavefront to another potential wavefront because phase is constant along wavefronts

Question 11

How will the phase delay look if the scattering is constructive and coherent

Answer 11

the same (mod 2𝜋)

Question 12

how will the phase delay look is the scattering is destructive and coherent

Answer 12

uniformly varying from 0 to 2𝜋

Question 13

under what condition will a beam remain a plane wave

Answer 13

if there is a direction for which coherent constructive interference occurs

Question 14

For relflected beams what are the conditiions for constructive and destructive interference

Answer 14

incident angle must equal reflected angle for constructive
if an angle is too big, symmetry disappears and the phases are all different

Question 15

What is an interference fringe

Answer 15

where beams have overlapped in space and time

Question 16

(in words) How is the crossing angle of beams related to the fringe spacing?

Answer 16

large crossing angle => closely spaced fringes

Question 17

What is the fringe spacing formula?

Answer 17

Λ = 2𝜋/2𝑘 sin 𝜃 = 𝜆/2 sin 𝜃

Question 18

What happens to the intensity pattern at a crossing angle of zero?

Answer 18

It becomes constant

Question 19

What is the minimum visible fringe spacing?

Answer 19

0.1mm

Question 20

What is intensity of interference

Answer 20

I(phase delay) = I0(1+mcos(phase delay))
where I0 = sum of squared amplitudes of interfering waves

Question 21

what is the formula for the visibility of fringes

Answer 21

𝑚 = (𝐼𝑚𝑎𝑥 − 𝐼𝑚𝑖𝑛)/(𝐼𝑚𝑎𝑥 + 𝐼𝑚𝑖𝑛)
where I max = sum of amplitudes squared and I min is difference of amplitudes squares

Question 22

How to you ensure high contrast/fringe visibility

Answer 22

By interfering beams of equal amplitudes

Question 23

What are the interferometers based on 2 beam interference

Answer 23

Michelson and Mach-Zehnder

Question 24

If the michelson mirros are exactly perpendicular, what will they produce

Answer 24

circular fringes

Question 25

what is the formula for the phase difference in a michelson interferometer

Answer 25

𝛿 = 2𝜋* 2(𝐿1 − 𝐿2)/𝜆

Question 26

When can white light fringes be observed in the michelson interferometer

Answer 26

when L1=L2 exactly

Question 27

What happens when you tilt the mirrors of the Michelson Interferometer

Answer 27

- vertical fringes appear in the field of view - moving the second mirror by half a wavelength moves each fringe by the fringe spacing difference

Question 28

If m fringes cross a line when M2 moves a distance d in the Michelson Interferometer, what is the wavelength

Answer 28

d= m𝜆/2 or 𝜆=2d/m

Question 29

What is the role of the beam splitter on the michelson interferometer

Answer 29

- reflection occurs off the front surface - transmitted beam passes through the beam splitter 3 times - reflected beam passes through once

Question 30

What is the role of the compensator plate in the michelson interferometer

Answer 30

- it is identical to the beam splitter to equalise the path length through glass

Question 31

How can we vary the phase delay for a michelson interferometer

Answer 31

introduce a gas cell into one of the paths with refractive index delta n

Question 32

What is the additional phase change for a michelson interferometer with a gas cell

Answer 32

phase change = 2𝜋*2(deltan-1)tcell/𝜆

Question 33

What happens when we misalign the mirrors of the michelson interferometer

Answer 33

the beams cross at an angle when they recombine at the beam splitter

Question 34

What is the intensity for crossed beams if the input to the michelson interferometer is a plane wave

Answer 34

I=I1+I2+Re{E0 exp[i(wt - kzcos𝜃-kxsin𝜃]E0*[-i(wt-kzcos𝜃+kxsin𝜃]}

Question 35

What does crossing beams do?

Answer 35

Maps delay onto position

Question 36

What happens when we change the path length of one arm in the michelson interferometer?

Answer 36

we introduce a 2kd phase shift so the fringes will shift by 2kd

Question 37

Describe the unbalanced Michelson Interferometer

Answer 37

- 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

Question 38

what is the cross term for an unbalanced michelson interferometer

Answer 38

Re{exp[2iphase(x,y) exp[-2ikxsin𝜃]}

Question 39

How is the Mach-Zehnder Interferometer usually operated

Answer 39

- 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

Question 40

What is a common use of the M-Z

Answer 40

to observe density variations in gas-flow patterns within wind tunnels, shock tubes and plasma chambers