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Ch 24
Wave Optics
concept questions #8, 11
problems #1, 3, 9, 15, 19, 31, 45, 48, 53
Light is a wave so interference can occur.
Interference effects for light are not easy to
observe because of the short wavelength.
Two conditions to observe sustained interference:
1) the sources must be coherent, they emit waves
with a constant phase with respect to each other.
2) The waves have identical wavelengths
Incoherent – when the phase between two
waves is not constant.
Ordinary light bulbs make incoherent light.
The conditions for constructive/destructive
interference only last for about 10-8s for
incoherent light.
Too fast to visually observe.
Easy way to produce coherent light sources.
Pass monochromatic light (light with 1
wavelength) through a slit.
The first slit creates a single wave front that
lights up two more slits, equally spaced from
the first.
The second pair of slits then act as a pair of
coherent light sources.
Young’s Double Slit experiment
• Observes interference pattern from light
emerging from two slits (pinholes)
• Observe alternating bright and dark parallel
bands (fringes).
– bright bands show constructive interference
– dark bands show destructive interference
Constructive interference occurs where the light hits the
screen in phase.
Destructive interference occurs where the light hits the
screen out of phase.
Path difference ( )
Path difference is the difference in distances the two
waves have to travel.
See pictures 24.3 and 24.4
= r2 – r1 = d sin
When is an integer multiple of the wavelength,
constructive interference occurs.
= d sin bright = m
m 0, 1, 2, 3,...
bright
corresponds to the angle to the bright fringe
Central bright fringe corresponds to m = 0. This is
called the zeroth-order maximum.
When is an odd multiple of /2, destructive
interference occurs and a dark fringe is present.
m 0, 1, 2, 3,...
= d sin dark = (m+ ½)
If m = 0, then = /2 and this corresponds to the
first dark spots next to the bright central fringe.
To simplify we make assumption that L >> d. The
length to the screen is much larger than the slit
separation. Also assume that d>> .
Using the previous assumptions, means that the
angles bright and dark are small.
For small angles:
sin
So our equations become:
d (y/L) = m or ybright = ( L/d)m
for bright fringes
m 0, 1, 2, 3,...
and
ydark
for dark fringes
L
1
(m
)
d
2
m 0, 1, 2, 3,...
Change of phase due to reflection
When light reflects off of a medium that has a
higher index of refraction than the initial
medium, the electromagnetic wave undergoes
a phase change of 1800.
See fig. 24.6 and 24.7
In figure 24.7 the two reflected beam interfere
with each other.
Due to the change of phase because of reflection,
thin films can produce an interference pattern.
Use rule that the wavelength in a medium of index of
refraction, n, is:
n = /n.
Let ray 1 be reflected from the top surface of the
film. Its phase changes by 1800. This is equivalent
to a path difference of /2.
Ray 2 pass through the film and reflects off the
bottom surface before coming back out the top.
If the thickness of the film is t, the extra distance
traveled by ray 2 is 2t.
Because ray 1 be reflected from the top
surface of the film, its phase changes by 1800.
This is equivalent to a path difference of /2.
If the extra distance traveled by ray 2 is an odd
multiple of n/2 the two waves recombine in
phase and constructive interference occurs.
2t = (m + ½) n m = 0, 1, 2, 3,…
subtituting n = /n we get:
2nt = (m + ½ )
m = 0, 1, 2, 3,…
Destructive interference in a thin film happens
when the extra distance traveled by ray 2 is a
multiple of n.
For destructive interference in a thin film:
2nt = m
m = 0, 1, 2, 3,…
See page 794 for thin film interference strategies.
Not the dependence on the number of phase
reversals.
See examples 24.2 and 24.3
Diffraction
When a wave front passes through a small
space or around a sharp edge, the shape of
the wave front changes.
For example when plane waves pass through a
thin slit, spherical waves come out.
See fig. 24.13 Fig. 24.14 shows the pattern
formed by a single narrow slit.
Single slit diffraction
When light passes through a slit, light from the
different portions of the slit will interfere with
light from other portions of the slit.
All the light at the slit is in phase. Notice that
some rays of the light have to travel farther than
others. See 24.17
Destructive interference occurs on the screen at
angles , where:
m
1, 2, 3,...
sin dark = m /a
a = slit width
Diffraction grating
Tool to analyze light sources.
Consists of a large number of equally spaced
parallel slits.
Made by scratching parallel lines on a glass plate.
Typical grating has several thousand lines per
centimeter.
Polarization
Light is a wave. (Electromagnetic wave)
Polarization is good evidence that
electromagnetic waves are transverse.
E-m waves consist of oscillating electric and
magnetic field oriented at 90 degree angles.
See fig. 24.24
Conventionally, the polarization corresponds to
the orientation of the electric field.
When charges vibrate, they act like tiny
antennas. The electric field will oscillate in the
direction of the vibration. Because vibration
can occur in all directions, the resultant e-m
wave is a superposition of the waves
produced by the vibrating charges.
This results in unpolarized light.
If the electric field vibrates in the same
direction every time, linearly polarized light is
produced.
See figure 24.25
Polarizer = material that polarizes light through the
selective absorption by aligned molecules.
The molecules absorb light that has an electric field
parallel to their length.
They transmit light that has an electric field
perpendicular to their length.
The direction perpendicular to the length of the
molecules is called the transmission axis.
Any light with an electric field perpendicular to the
transmission axis is absorbed. See figure 24.26
Polarizing light reduces the intensity of the light
that passes through the polarizer.
When unpolarized light passes through a
polarizer, half the intensity is transmitted.
When light reaches a second polarizer, (called an
analyzer), the transmitted beam’s intensity
depends on the angle between polarizers.
I = I0 cos2
Figure 24.27
All the light is blocked when the two polarizers have
their transmission axis at 900 angles.
http://www.loncapa.org/~mmp/kap24/polarizers/Polarizer.htm
Polarization by reflection
When unpolarized lights is reflected from a
surface, the reflected beam is either completely
polarized, partially polarized, or unpolarized
depending on the angle of incidence.
For one special angle of incidence, the reflected
light is completely polarized.
See figure 24.28
Brewster’s angle is the angle of incidence that
results in the reflected beam being totally
polarized.
n = tan p
n is the index of refraction of the reflecting
medium.
-1 n
=
tan
p
0
For glass n = 1.52
=
56.7
p
For water n = 1.33 p= 53.10