From Last time…
Two-source
interference:
Week3HW on Mastering Physics
due Fri. Sep. 18
Week2HW due Fri. Sep. 11
Diffraction grating
Diffraction = interference
from many sources
New topic: Diffraction
only one slit, but “wide”
• Interference-like pattern from
a single slit.
For a slit:
central width ~ 2


a
Long wavelength:
wide pattern
Short wavelength
narrow pattern
Huygen’s principle
• Huygen’s principle:
each portion of the
slit acts as a source
of waves
• These sources
interfere according to
path-length
difference.
Thursday, Sep. 10
Physics 208, Lecture 3
3
Overlapping diffraction patterns
• Two sources ->two
diffraction patterns.
• Width central max
determined by
aperture.
Angular
separation

• Larger aperture gives
better angular
resolution
• For a circular aperture (e.g. lens)
min 1.22

D
36” Lick refractor at UC-Berkeley
D
Large aperture
-> good angular resolution
min 1.22
Thursday, Sep. 10
Physics 208, Lecture 3

D
5
Diffraction from other objects
Light diffraction by pinhead
• General effect
• Clearest w/single wavelength
Thursday, Sep. 10
Physics 208, Lecture 3
6
Interference summary
• Waves start in phase
• Travel different distances (extra path length = )
• No longer in phase when combined (Phase diff )
Longer path
Here,  = λ/2
Phase diff π
Crest aligns with trough
Destructive interference
Shorter path
Thursday, Sep. 10
Physics 208, Lecture 3
7
Another source of phase difference
• In some cases reflection gives phase shift
n1
n2>n1
π phase shift
n1
no phase shift
n2<n1
Thin film interference
Black
Colors
changing
with
thickness
Thursday, Sep. 10
Physics 208, Lecture 3
9
180˚ (π radians) phase shift from reflection

no phase shift from reflection
air: n=1
t
n>1
Extra path
length~2t
 /n
Thin film
air: n=1
Contributions to the phase difference
• Phase difference from reflection
– Top reflection has π phase shift, bottom not
• Phase difference from path length difference
– Path length difference = 2t
2t
– Gives phase difference 2
 /n
Thursday, Sep. 10
Physics 208, Lecture 3
10
  2
Phase difference =
Reflection
phase shift


1 
2t  m  

2 n
2t  m

n
2t

 /n
2m
constructive
2m  1 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
Physics 208, Lecture 3
11
Biological iridescence
• Some organisms seem to reflect incredibly vivid colors.
Not by pigment, but interference!
Thursday, Sep. 10
Physics 208, Lecture 3
12
constructive  446nm

Thursday, Sep. 4
Phy208 Lecture 2
13
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
What is a light ray?
• Light ray is a line in the direction along
which light energy is flowing.
Wavefronts
(crests of waves)
Ray enters eye -> you can see the light source
What does a light ray do?
• Light rays travel forever in straight line
unless they interact with matter
(reflection, refraction, absorption)
What about diffraction?
• Light really behaves as a wave
• The concept of a light ray is an approximation
i.e. a lie
Wavelength << aperture size,
rays are good approximation
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).
Interaction of light with matter
Absorption
Reflection
Reflection/refraction
occur at interfaces
between different materials
And all occur
simultaneously
Refraction
Reflection and Refraction
• Direction of light can be changed by
– Reflection (lets you see an object)
– Refraction (transmits light thru object)
… at an interface between different materials
Air
Interface
Plastic
• 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
When are materials different?
• For reflection/refraction
– 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.
c
v
n
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
Diamond
2.41
c=speed of light in vacuum
What do you think?
Pyrex stirring rod (n=1.46) dipped into beaker of
Wesson oil (n=1.46). What happens to the rod?
A. Appears dark
Beaker of
Wesson oil
B. Appears bright
C. Appears invisible
D. Appears curved
E. Appears inverted
Pyrex
stirring rod
No reflection/refraction if index of refraction is same.
Reflection
• Angle of incidence
= angle of reflection
i
Incident
ray
r
Reflected
ray
• Multiple reflections
• Apply i=r at each surface
–trace ray
Why i=r?
• Christian Huygens modeled this in 1690
– Said that each point on wavefront acts as source of
spherical wavelets
– Superposition of wavelets gives reflected plane
wave such that i=r
i
r
What about refraction?
• Refraction occurs when light moves into
medium with different index of refraction.
• Result: light direction bends according to
Snell’s law
n1 sin 1  n2 sin 2
i,1
r

n1
n2
2
Angle of refraction
Why Snell?
• Can analyze in exactly the same way
• Light moves at different speed in different media
i
r
n1
2
n2>n1
v2<v1
Refraction angle
n1
Reflected
ray
v2<v1
n2 >n1
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
Quick quiz
Which of these fluids has the
smallest index of refraction
(highest light speed)?
A
B
A. Fluid A
B. Fluid B
C. Fluid C
D. All equal
C
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
2
n1 sin 1  n 2 sin  2
1=45˚
n1
sin 1  0.94
n2
n1

 2  arcsin  sin 1  70Þ
n 2

sin  2 
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.
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° (sin = 1)
For water:
1
sin c 
 0.75  c  48.75Þ
1.333
Optical Fibers
• 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
The cladding has a
lower n than the core