Wave Optics
331
(a) If
1
2
3
45 ,
90
, and
0
θ
θ
θ
=
°
=
°
=
°
, then
(
)
(
)
2
2
2
cos 45 cos
90
45
cos
0
90
0
f
i
I
I
=
°
° −
°
° −
° =
(b) If
1
2
3
0 ,
45
, and
90
θ
θ
θ
=
°
=
°
=
°
, then
(
)
(
)
2
2
2
cos 0 cos
45
0
cos
90
45
0.25
f
i
I
I
=
°
° −
°
° −
° =
24.63
In the figure at the right, observe that the path difference
between the direct and the indirect paths is
(
)
2
2
2
2
2
x
d
h
d
d
δ
=
−
=
+
−
With a phase reversal (equivalent to a halfwavelength
shift) occurring on the reflection at the ground, the
condition for constructive interference is
(
)
1 2
m
δ
λ
=
+
, and the condition for
destructive interference is
m
δ
λ
=
. In both cases, the possible values of the order
number are
m
.
0, 1, 2,
=
…
(a)
The wavelengths that will interfere constructively are
1 2
m
δ
λ
=
+
. The longest of
these is for the
case and has a value of
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 Spring '09
 Physics, Work, Cos, WAVE OPTICS, phase reversal

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