135
10)
Fig 3
)
t
cos(
sin
A
E
1
β

ω
β
β
=
 (14)
Similarly, the secondary slit will produce a field
)
t
cos(
sin
A
E
1
2
Φ

β

ω
β
β
=
 (15)
at the point P, where
θ
λ
π
=
Φ
sin
d
2
1
represents the phase difference between the
disturbances from two corresponding points on the slits; by corresponding points we
imply pair of points like (A
1
,B
1
), (A
2
,B
2
)… … ., which are separated by a distance d.
Hence the resultant field will be
[ ]
)
t
cos(
)
t
cos(
sin
A
E
E
E
1
2
1
Φ

β

ω
+
β

ω
β
β
=
+
=
which represents the interference of two waves each of amplitude
β
β
sin
A
and
differing in phase by
1
. Above equation can be written as
)
2
t
cos(
cos
sin
A
E
1
Φ

β

ω
γ
β
β
=
where
±
=
θ
λ
π
=
Φ
sin
d
2
1
.
The intensity distribution will be of the form
γ
β
β
=
2
2
2
0
cos
sin
I
4
I
 (16)
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where
2
2
0
sin
I
β
β
represents the intensity distribution produced by one of the slits. As
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 Fall '09
 LIND
 Diffraction, Wavelength, Sin

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