1
Physics 1C
Winter 2009
Class Notes
Week 7
Walter Gekelman
Interference of Light:
If two vectors of equal magnitude and opposite direction are added their sum is zero.
This is the basic principle of the interference of light.
E
=
E
0
cos(
kz
!
"
t
)
!
E
0
cos(
kz
!
"
t
)
=
0
.
This is the electric field of two waves of light
traveling in the same direction but the E field vector of one is pointing up and that of the
other pointing down.
This is also the same as saying there are two waves out of phase
by 180 degrees:
E
=
cos
kz
!
"
t
(
)
+
cos
kz
!
"
t
+
#
(
)
if
#
=
$
then
E
=
cos
kz
!
"
t
(
)
!
cos
kz
!
"
t
(
)
If we use our complex
notation:
!
E
=
E
0
e
i kz
!
"
t
(
)
+
E
0
e
i kz
!
"
t
+
#
(
)
=
E
0
e
i kz
!
"
t
(
)
+
E
0
e
i
#
e
i kz
!
"
t
(
)
,
#
=
$
e
i
$
=
cos
$
+
i
sin
$
=
!
1
E
=
Re
!
E
=
0
Consider a source of monochromatic light, for example a laser.
The light is expanded by
lenses, to make a plane wave traveling in the x direction.
The light then hits a screen with
two narrow slits cut in it.
The slits are aligned with the z axis and are very, very long.
There is a photosensitive screen a distance L away from the slits. L is much larger than d,
the distance between the slits.
Each beam will travel a different distance to the screen.
Let us write the relationship between the phase difference, which is important for
interference, in terms of the path difference.
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2
(1)
!
phase
(
)
=
!
"
=
2
#
$
!
path
(
)
.
This is because the path is going to be some
number ( for example 320.7 ) wavelengths of the light.
Each wavelength is a phase
difference of 2
π
.
If the two beams combine in phase at a position on the wall you get a
bright spot.
If the beams are
π
out of phase they destructively interfere and you get
darkness.
This is illustrated in the figure below:
We wish to make a plot of the intensity of light on the film for any position y on the
wall.
If we redraw the diagram for 2 rays of light:
If d <<<L then the two lines S
1
P and S
2
P are nearly equal. (They are like the radius of a
circle centered at P).
This makes the difference in path between the rays dsin
θ
as shown.
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 Winter '07
 Whitten
 Light, Wavelength, ray II

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