Phase shift due to reflection - Physics Courses
Interference effects
6.1 Interference and Diffraction II.
recombined
Thin film interference
Michelson Interferometer
X?ray Diffraction
Coherent
light
Interference effects
phase shifted
Thin film interference
Phase shift due to reflection
phase shift 0
phase shift p
n1
?
?
In thin film interference the phase difference is due to
reflection at either side of a thin film of transparent
material.
The phase difference is due to two factors:
¨C Path difference through the film (corrected for the
change in speed of light in the material)
¨C Phase shift at the interface
Interference due to thin film
reflection (e.g. film in air)
Beams 1 and 2 reflected off the front
and back surfaces of a thin film
combine to show interference effects.
?
?
A net phase shift difference of p due
to reflection
Beam 2 has a phase shift due to
path difference
n1
n2
n2
n1 > n2
n1 < n2
? When a wave is reflected in going from a medium with a lower
refractive index to a higher refractive index the phase is shifted by p.
? When a wave is reflected in going from a medium with a higher
refractive index to a lower refractive index, the phase is not shifted.
Conditions for constructive and
destructive interference (film in air)
Constructive interference
1 l
2d = ( m + )
2 n
l/n is the speed of light in the
media with refractive index n.
The condition involves the half?
integer wavelength because of the
phase shift due to reflection
Destructive interference
2d = m
l
n
The condition involves integer
wavelengths because of the phase
shift of p
As d?> 0, there is destructive
interference due to the phase shift
Phase shift p
Phase shift 0
1
Soap film Example 37.4
A rectangular loop of wire 20 cm square is dipped into a soap solution an then
held vertically, producing a soap film whose thickness varies linearly from
essentially zero at the top to 1.0¦Ìm at the bottom. If the film is illuminated
with 650 nm light how many bright bands will appear?
Anti?reflective Coating
no coating
Soap film interference pattern
Black film
Anti?reflective Coating
Anti?reflective coatings consists of a thin?layer
of material with a refractive index in between
that of air and glass. Destructive interference
between light reflected at the two surfaces
reduces the intensity of reflected light.
Anti?reflective coatings are used
to reduce reflections at the air?glass
interface.
The phase shift is p at both surfaces.
Therefore no phase shift difference
Condition for destructive interference.
d
anti?reflective
coating
n1=1.00
Question
1 l
2d = ( m + )
2 n2
< n2 < n3
Compact discs
An anti?reflective coating of MgF2 (n=1.38) is used on a glass surface to
reduce reflections. Find the minimum thickness of the coating that
can be used for green light (l=550 nm).
Digital information stored on pits in
tracks.
Spacing between tracks 1.6mm
2
optical compact discs CD
high reflectance low reflectance
Question
A cd is made out of a plastic with a refractive index of 1.55.
If the cd is scanned with a laser with a wavelength of 780
nm how high should the pits on the surface be for
destructive interference.
d
reflected
light
Coding of information read out by a laser beam.
Reflection from tracks is modulated by destructive interference.
Michelson Interferometer
.
d
moving the mirror by a distance d
produces fringe shifts, from bright to
dark to bright.
The no. of fringe shifts, m is related to
the change in the path length.
Question
A Michelson interferometer uses a hydrogen emission line
at 486.1 nm. As you move one mirror, 530 bright
fringes pass a fixed point in the viewer. How far did
the mirror move?
2d = m l
Interference pattern
X?ray diffraction
NaCl Crystal ¨C an ordered array of atoms
0.56 n
? X?ray diffraction uses x?rays to scatter from atoms in a
crystal.
? The crystal acts as a 3?dimensional grating.
? The pattern of spots in the diffracted beam contains
information about the 3?dimensional structure of atoms in
the crystal.
3
X?ray diffraction pattern of NaCl
Diffraction of x?rays from a crystal.
Each atom acts as a wave source.
Fig. 27?11, p.883
Bragg condition
Question
An x?ray source with a wavelength of 0.154 nm passes
through a NaCl crystal and is shows a first order
diffraction peak at an angle of 15o away from the central
maximum. What is the spacing of the crystal plane
responsible for the diffraction?
X?rays are scattered from planes of atoms in a crystal lattice spaced a
distance d apart.
The condition for reflection is the condition for constructive interference of x?
rays scattered from different planes (pathlength diffference =ml)
2d sin q = ml
Note the difference in the definition of ¦È
DNA structure
determined by
x?ray diffraction
X?ray diffraction pattern from a crystalline fiber of DNA. Watson
And Crick used this data to deduce the structure of the DNA molecule
4
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