Transcript HP unit 12 - wave optics student handout

Wave Optics
This first half of unit deals with the wave aspects of
light, where only wave theory can explain the
phenomena and particle/quantum theory falls short.
The three primary topics of wave optics is
interference, diffraction, and polarization.
Interference – Young’s Double
Slit Experiment 1801
Prior to this experiment, the particle theory was the
dominant view.
Thomas Young devised an experiment using 2 slits to act
as two point sources.
What would particle
theory (or rays) predict
after light passed through
openings onto screen?
Particle theory could NOT explain why multiple
lines of light appeared on screen but wave could.
Creating a bright
region directly
behind barrier
makes sense since
light waves travel
same distance, but
what about other
areas?
The interference occurs because each point on the
screen is not the same distance from both slits.
Path length is the extra
distance one of the
waves travels to meet
the other on the screen.
This assumes that paths
(d1 & d2 ) are nearly parallel
and that L>>d
For Constructive Interference:
A bright fringe is produced, via C. I., if the path difference is
zero or some integral multiple of the wavelength where
– m = 0, ±1, ± 2, …where m is called the order number
• When m = 0, it is the zeroth order maximum
• When m = 1, it is called the first order maximum, etc
For Destructive Interference:
A dark fringe is observed when
the path difference equals an odd
half wavelength multiple
–m = 0, ± 1, ± 2,
Conditions for interference
For sustained interference between two
sources of light to be observed, there are
two conditions which must be met
– The sources must be coherent, meaning they
must maintain a constant phase with respect
to each other
– The waves must have identical wavelengths
There is also a relationship to the location of the
fringes on the screen (y)
Assume L>>d
where θ is
small and
sinθ  tanθ
Intensity on screen for 2 slits
Between the maxima and the minima, the
interference varies smoothly.
Monochromatic light falls on two slits that are 0.0525mm
apart producing an interference pattern on a screen
6.50m away with bright fringes that are 7.36cm apart.
What is the wavelength of light?
Diffraction
Recall that diffraction involves waves bending
around obstacles or passing through openings
Diffraction by a single slit or object
Similar to 2 slits, obstacle or 1 slit causes
diffraction. Slit yields same result as barrier.
Single Slit Diffraction explained
How does a
single slit
produce a series
of bands like
double slit?
Consider a slit of width, w. As a wave front approaches, imagine
each portion of the slit as a source of waves.
If we consider the rays that
travel northeast through the
slit towards a screen. Note
that rays aren’t parallel.
If we look at ray 5 (just below
edge of slit) and ray 3 (center
of slit),
In fact, another ray just below ray 5 and just below 3
will also cancel
Single slit pattern
How wide is a central diffraction peak on a screen
3.60m behind a slit, with a width of 0.0344 mm,
when illuminated by 440nm light?
Multiple slits produce an array of colors
(diffraction grating) depending on the angle you
view the ‘screen’.
White light reflected from closely
spaced grooves in CD causes
constructive interference in certain
directions for different colors.
Iridescence of peacock feathers is caused by
light reflected from complex layered surface.
Different colors of white light interfere at different locations.
Resolution of single slit
and circular apertures
The ability of a lens to produce distinct images of 2
point objects very close together is called
resolution. The closer the 2 objects can be seen as
distinct, the higher the resolution.
Because of
diffraction, there is a
limit on the resolution
by optical devices
such as your eye or a
telescope.
Resolving Power
How close can two
points of light be to
still be resolved as 2
distinct light points
instead of one?
Two sources of light
are just resolvable
when the
S2
θ
S1
2 sources
far apart
2 sources are
close enough
together that
they are ‘just
resolved’
2 sources
so close
that they are
not resolved
A motorcycle has twin headlights which emit light
with an average wavelength of 550nm. The diameter
of the pupil is 4.3mm, at what distance can the two
headlights be resolved if the headlights are a
distance 20cm apart?
The camera on a spy satellite has a lens with a diameter of
1.5m. This satellite is in low earth orbit about 2.9x105m above
the surface of the Earth. Determine the approximate size of
the smallest feature the camera can resolve when taking a
picture of something on the Earth's surface (assume blue
light with a λ = 400nm, and ignore the effect of the Earth's
atmosphere)
Is it easier to resolve two headlights
during the night or day?
Hint: What is the difference with your pupils
during the day vs the night?
Application: The Eye
Chart and 20/20 vision
The chart is based on a
standard distance of 6.0m
or 20 feet.
20/20 vision means you
can distinguish the letters
on the fourth line up (8)
from the bottom at a
distance of 20ft.
The basic scheme is that
the letters two rows down
are half the size, and two
rows up twice the size, etc
Thin Films
Essentially, part of an incident wave is reflected off
the top surface of film while the other part is
transmitted into the thin film where it reflects off
bottom surface (of film). Waves are NEARLY parallel.
Relating wavelength to index of refraction
When light enters new medium,
v and λ both change
Not only can reflection cause a phase shift so that
waves are out of step, but so can the distance
traveled in the film itself.
Thickness of Soap Bubble Skin
What is minimum thickness t of soap
bubble if it appears green (l=540 nm)
at the point of front surface closest to
viewer? Assume nsoap = 1.35.
Example2
Light (λ=550nm) moves
from air to a film of silicon
oxide which sits on
silicon. What minimum
thickness of film
must be present to get zero
reflection?
A similar effect takes place when a shallowly curved
piece of glass is placed on a flat one. When viewed
from above, concentric circles appear that are called
Newton’s rings.
Example: Two long, flat pieces of glass plates are placed one
on top of the other separated only by a thin piece of plastic at
one end.
Side view
If there are 37 dark and 37 bright lines
starting from the end of the pair of
glass plates that are touching to the
other, how thick is the piece of plastic
when illuminated by a sodium lamp
(λ=589nm)?
How a laser ‘reads’ a CD
Polarization (only light waves)
Light waves oscillate in all planes coming from a
source. Sunlight is considered to be unpolarized.
Polarized
light
oscillates in
one
particular
plane.
When light reflects off surface, it
polarizes in that plane.
Polarized Filters
Polarized filters only allow one plane of light to
pass through, similar to a picket fence. A
vertical polarizer will only allow vertically
polarized light to pass.
This means that if initially unpolarized light
passes through crossed polarizers, no light
will get through the second one.
Sunglasses