Set Up:
Since the values of
m
are rather large, don’t use Eq.(26.6).
For bright fringes,
For dark fringes,
For the fifth bright fringe (not counting the central bright spot),
and for the eighth dark fringe,
Solve: (a)
and
(b)
and
26.7.
Set Up:
The values of
are much smaller than the distance
R
to the screen, so the approximate expression
is accurate.
Solve:
Reflect:
This is a visible wavelength.
26.8.
Set Up:
The value of
is much smaller than
R
and the approximate expression
is accurate.
Solve:
26.9.
Set Up:
Bright fringes are located at
when
Dark fringes are at
and
For the third bright fringe (not counting the central
bright spot),
For the third dark fringe,
m
5
2.
m
5
3.
y
5
R
tan
u
.
d
sin
u 5
A
m
1
1
2
B
l
y
m
V
R
.
y
m
5
R
m
l
d
,
l 5
c
f
5
3.00
3
10
8
m
/
s
6.32
3
10
14
Hz
5
4.75
3
10
2
7
m.
d
5
20
R
l
y
20
5
1
20
21
1.20 m
21
502
3
10
2
9
m
2
10.6
3
10
2
3
m
5
1.14
3
10
2
3
m
5
1.14 mm
y
20
5
10.6
3
10
2
3
m.
y
m
5
R
m
l
d
y
20
l 5
d
D
y
R
5
1
0.460
3
10
2
3
m
21
2.82
3
10
2
3
m
2
2.20 m
5
590 nm
D
y
5
y
m
1
1
2
y
m
5
R
l
d
.
y
m
5
R
m
l
d
y
m
y
5
R
tan
u 5
7.16 cm.
u 5
5.45°.
sin
u 5
A
7
1
1
2
B
1
l
d
2
5
0.0949
y
5
R
tan
u 5
1
75.0 cm
2
tan
3.63°
5
4.75 cm
u 5
3.63°.
sin
u 5
5
1
l
d
2
5
5
1
525
3
10
2
9
m
0.0415
3
10
2
3
m
2
5
0.0633
m
5
7.
m
5
5
d
sin
u 5
A
m
1
1
2
B
l
.
d
sin
u 5
m
l
.
y
m
5
R
tan
u
m
.
l
/
2.
d
5
l
4
5
1.36 m
4
5
34.0 cm.
2
d
5
l
2
l
/
2.
d
5
l
2
5
1.36 m
2
5
68.0 cm.
2
d
5 l
l
.
l 5
v
f
5
340.0 m
/
s
250.0 Hz
5
1.36 m
6
2,
c
.
6
1,
m
5
0,
path difference
5
A
m
1
1
2
B
l
,
6
2,
c
.
6
1,
m
5
0,
path difference
5
m
l
,
180°
r
1
r
2
r
2
2
r
1
d
5
l
2
5
1.36 m
2
5
68.0 cm.
2
d
5 l
l
.
d
5
l
4
5
1.36 m
4
5
34.0 cm.
2
d
5
l
2
l
/
2.
l 5
v
f
5
340.0 m
/
s
250.0 Hz
5
1.36 m
262
Chapter 26
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Solve: (a)
(b)
and
Reflect:
The third dark fringe is closer to the center of the screen than the third bright fringe on one side of the cen
tral bright fringe.
26.10.
Set Up:
At large distances from the antennas the equation
gives the
angles where maximum intensity is observed and
gives the angles where
minimum intensity is observed.
Solve: (a)
(b)
26.11.
Set Up:
is very small for these dark lines and the approximate
expression
is accurate. Adjacent dark lines are separated by
Solve:
26.12.
Set Up:
Water has
In water the wavelength is
is very small for these dark lines
and the approximate expression
is accurate. Adjacent dark lines are separated by
Solve:
is smaller in water and the
dark lines are closer together when the apparatus is immersed in water.
26.13.
Set Up:
The largest value
can have is 1.00. Bright fringes are located at angles
given by
Solve: (a)
For
Therefore, the largest
m
for fringes on
the screen is
There are
bright fringes, the central one and 19 above and 19 below it.
(b)
The most distant fringe has
and
Reflect:
For small
the spacing
between adjacent fringes is constant but this is no longer the case for larger
angles.
D
y
u
u 5 6
73.3°.
sin
u 5
m
l
d
5 6
19
1
5.85
3
10
2
7
m
0.0116
3
10
2
3
m
2
5 6
0.958
m
5 6
19.
2
1
19
2
1
1
5
39
m
5
19.
m
5
d
l
5
0.0116
3
10
2
3
m
5.85
3
10
2
7
m
5
19.8.
sin
u 5
1,
m
5
d
sin
u
l
.
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 Spring '09
 RODRIGUEZ
 Physics, Diffraction, Wavelength, Sin, NM, path difference

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