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402
Interference of Light Waves
P37.60
Bright fringes occur when
2
1
2
t
n
m
=+
F
H
G
I
K
J
λ
and dark fringes occur when
2
t
n
m
=
F
H
G
I
K
J
.
The thickness of the film at
x
is
t
h
x
=
F
H
G
I
K
J
A
.
Therefore,
x
hn
m
bright
F
H
G
I
K
J
A
2
1
2
and
x
m
hn
dark
=
A
2
.
FIG. P37.60
P37.61
Call
t
the thickness of the film. The central maximum
corresponds to zero phase difference. Thus, the added
distance
∆
r
traveled by the light from the lower slit must
introduce a phase difference equal to that introduced by
the plastic film. The phase difference
φ
is
φπ
=
F
H
G
I
K
J
−
21
t
n
a
af
.
The corresponding difference in
path length
∆
r
is
∆
r
t
nt
n
a
a
a
=
F
H
G
I
K
J
=
F
H
G
I
K
J
−
F
H
G
I
K
J
=−
π
2
2
1
.
Screen
θ
y'
Zero
order
m
= 0
L
Thin
film
α
∆
r
d
FIG. P37.61
Note that the wavelength of the light does not appear in this equation. In the figure, the two rays
from the slits are essentially parallel.
Thus the angle
may be expressed as
tan
==
′
∆
r
d
y
L
.
Eliminating
∆
r
by substitution,
′
=
−
y
L
tn
d
1
gives
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Light

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