New topic: Diffraction
only one slit, but “wide”
From Last time…
Two-source
interference:
•  Interference-like pattern from
a single slit.
For a slit:
λ
a
θ central width ~ 2
Diffraction grating
Week3HW on Mastering Physics
due Fri. Sep. 18
€
Diffraction = interference
from many sources
Week2HW due Fri. Sep. 11
Huygen’s principle
Long wavelength:
wide pattern
Short wavelength
narrow pattern
Overlapping diffraction patterns
•  Two sources ->two
diffraction patterns.
•  Huygen’s principle:
each portion of the
slit acts as a source
of waves
•  These sources
interfere according to
path-length
difference.
•  Width central max
determined by
aperture.
Angular
separation
θ
•  Larger aperture gives
better angular
resolution
•  For a circular aperture (e.g. lens)
Thursday, Sep. 10
Physics 208, Lecture 3
θ min = 1.22
λ
D
3
€
36” Lick refractor at UC-Berkeley
Diffraction from other objects
D
Light diffraction by pinhead
Large aperture
-> good angular resolution
θ min = 1.22
Thursday, Sep. 10
Physics 208, Lecture 3
•  General effect
•  Clearest w/single wavelength
λ
D
5
Thursday, Sep. 10
Physics 208, Lecture 3
6
€
1
Another source of phase difference
Interference summary
•  In some cases reflection gives phase shift
•  Waves start in phase
•  Travel different distances (extra path length = δ)
•  No longer in phase when combined (Phase diff φ)
n1
n2>n1
π phase shift
Longer path
Here, δ = λ/2
Phase diff π
Crest aligns with trough
Destructive interference
Shorter path
Thursday, Sep. 10
Physics 208, Lecture 3
n1
n2<n1
no phase shift
7
180˚ (π radians) phase shift from reflection
λ
Thin film interference
no phase shift from reflection
air: n=1
Black
t
n>1
Extra path
length~2t
λ /n
Thin film
air: n=1
Contributions to the phase difference
•  Phase difference from reflection
Colors
changing
with
thickness
Thursday, Sep. 10
Physics 208, Lecture 3
9
–  Top reflection has π phase shift, bottom not
•  Phase difference from path length difference
–  Path length difference = 2t
–  Gives phase difference 2π
Thursday, Sep. 10
2t
λ /n
Physics 208, Lecture 3
10
€
Phase difference =
π + 2π
Reflection
phase shift
€

1 λ
2t =  m + 

2 n
2t = m
λ
n
2mπ
2t
(λ /n )
constructive
(2m + 1)π destructive
€
Convert
to phase
(m = 0,1,2…)
(m = 0,1,2…)
# wavelengths in
extra path
length
€
constructive interference
destructive interference
€
What happens when:
t << all λ in light?
Constructive int. condition for some λ?
€
Thursday, Sep. 10
Biological iridescence
=
Physics 208, Lecture 3
11
•  Some organisms seem to reflect incredibly vivid colors.
Not by pigment, but interference!
Thursday, Sep. 10
Physics 208, Lecture 3
12
2
Waves and geometry
•  Interference and diffraction demonstrate that
light is a wave.
•  Doesn’t always appear as a straight ‘ray’ of light
… but sometimes it almost does!
Geometric optics:
Tracing the path of light rays
λconstructive = 446nm
€
Thursday, Sep. 4
Phy208 Lecture 2
13
What is a light ray?
•  Light ray is a line in the direction along
which light energy is flowing.
What does a light ray do?
•  Light rays travel forever in straight line
unless they interact with matter
(reflection, refraction, absorption)
Wavefronts
(crests of waves)
Ray enters eye -> you can see the light source
What about diffraction?
•  Light really behaves as a wave
•  The concept of a light ray is an approximation
i.e. a lie
Light rays from point source
•  Light rays are not always parallel.
–  E.g. light bulb visible from all directions
–  Rays must be traveling in all directions
Light ray perpendicular to local
wavefront (crest of wave).
Wavelength << aperture size,
rays are good approximation
3
Reflection and Refraction
Interaction of light with matter
•  Direction of light can be changed by
Absorption
–  Reflection (lets you see an object)
–  Refraction (transmits light thru object)
Reflection
… at an interface between different materials
Reflection/refraction
occur at interfaces
between different materials
•  Ray  is the incident ray
•  Ray  is the reflected ray
•  Ray  is refracted into the
lucite
•  Ray  is reflected inside the
lucite
•  Ray  is refracted as it enters
the air from the lucite
Air
Refraction
Interface
Plastic
And all occur
simultaneously
What do you think?
When are materials different?
•  For reflection/refraction
Material
–  materials are different if they have
different index of refraction
–  Light propagates at different speed
in different materials.
–  Due to interaction of
electromagnetic wave with atoms
in material.
Index
of refraction
Vacuum
1.00 exactly
Air (actual)
1.0003
Air (accepted)
1.00
Ice
1.31
Water
1.33
Ethyl Alcohol
1.36
Oil
1.46
Pyrex glass
1.46
Crown glass
1.52
Polystyrene plastic
1.59
Flint glass
1.66
c
n c=speed of light in vacuum
Diamond
v=
2.41
Pyrex stirring rod (n=1.46) dipped into beaker of
Wesson oil (n=1.46). What happens to the rod?
Beaker of
Wesson oil
A.  Appears dark
B.  Appears bright
C.  Appears invisible
D.  Appears curved
Pyrex
stirring rod
E.  Appears inverted
No reflection/refraction if index of refraction is same.
€
Why θi=θr?
•  Christian Huygens modeled this in 1690
Reflection
•  Angle of incidence
= angle of reflection
θi
Incident
ray
θr
Reflected
ray
–  Said that each point on wavefront acts as source of
spherical wavelets
–  Superposition of wavelets gives reflected plane
wave such that θi=θr
θi
θr
•  Multiple reflections
•  Apply θi=θr at each surface
– trace ray
4
What about refraction?
•  Refraction occurs when light moves into
medium with different index of refraction.
•  Result: light direction bends according to
Snell’s law
Why Snell?
•  Can analyze in exactly the same way
•  Light moves at different speed in different media
θi
n1 sin θ1 = n 2 sin θ 2
θr
n1
θi,1
θr
€
n1
n2
n2>n1
v2<v1
θ2
θ2
Angle of refraction
Quick quiz
Refraction angle
Which of these fluids has the
smallest index of refraction
(highest light speed)?
n1
n1
Reflected
ray
v2<v1
n2 >n1
Reflected
ray
v2>v1
n2 < n1
slower in medium 2
faster in medium 2
n2>n1
Refracted ray bent
toward normal
n2<n1
Refracted ray bent
away from normal
Numerical Example
A beam of light is traveling underwater, aimed up at the
surface at 45˚ away from the surface normal. Part of
it is reflected back into the water, and part is
transmitted into the air.
Air
n2=1.00
Water
n1=1.33
θ2
n1 sin θ1 = n 2 sin θ 2
n
sin θ 2 = 1 sin θ1 = 0.94
n2
n

θ 2 = arcsin 1 sin θ1  = 70˚
 n2

θ1=45˚
A
B
A.  Fluid A
B.  Fluid B
C
C.  Fluid C
D.  All equal
Quick quiz
A trout looks up through
the surface at the
setting sun, and at the
moon directly
overhead.
He sees
n2=1.0
n1=1.33
A.  Moon directly overhead, sun ~ parallel to water surface
B.  Moon directly overhead, sun ~ 40˚ above water surface
C.  Moon ~ 40˚ from vertical, sun ~ parallel to water surface
D.  Moon and sun aligned at 40˚ from vertical.
€
5
Total Internal Reflection
•  Is possible when light is directed from n1 > n2
⇒ refracted rays bend away from the normal
•  Critical angle: angle of
incidence that will result in
an angle of refraction of
90° (sinθ2 = 1)
For water:
sin θ c =
Optical Fibers
The cladding has a
lower n than the core
•  Plastic or glass light pipes
•  Applications:
–  Medicine: endoscope (light can be
directed even if bent and the
surgeon can view areas in the body
using a camera.)
–  Telecommunications
1
= 0.75 ⇒ θ c = 48.75˚
1.333
€
6