CHAPTER 37 INTERFERENCE AND DIFFRACTION
ActivPhysics
can help with these problems: Activities in Section 16, Physical Optics
Section 37

2: DoubleSlit Interference
Problem
1.
A doubleslit system is used to measure the wavelength of light. The system has slit spacing
d
=
15 m
m
and slitto
screen distance
L
m
=
=
2 2
1
.
m. If the
maximum in the interference pattern occurs 71
.
cm from screen center, what is
the wavelength?
Solution
The experimental arrangement and geometrical approximations valid for Equation 372a are satisfied for the situation and
data given, so
l
m
=
=
=
y
d mL
bright
cm
m
m
nm.
=
=
=
( .
.
)(
)
71
2 2
15
1
484
(In particular,
l
q
¿
d
and
1
2
3 23
10
185
=
×
=
°

.
.
is small.)
Problem
2.
A doubleslit experiment with
d
L
=
=
0 025
75
.
mm and
cm uses 550nm light. What is the spacing between adjacent
bright fringes?
Solution
Assume that the geometrical arrangement of the source, slits, and screen is that for which Equations 372a and b apply. The
spacing of bright fringes is
∆
y
L d
=
=
=
l
=
=
(
)(
) (
.
)
.
550
75
0 025
165
nm
cm
mm
cm.
Problem
3.
A doubleslit experiment has slit spacing 012
.
mm. (a) What should be the slittoscreen distance
L
if the bright fringes
are to be 5 0
.
mm apart when the slits are illuminated with 633nm laser light? (b) What will be the fringe spacing with
480nm light?
Solution
The particular geometry of this type of doubleslit experiment is described in the paragraphs preceding Equations 372a
and b. (a) The spacing of bright fringes on the screen is
∆
y
L d
L
=
=
=
l
=
=
,
( .
)(
) (
)
.
so
mm
mm
nm
cm.
012
5
633
94 8
(b) For
two different wavelengths, the ratio of the spacings is
∆
∆
′
=
′
y
y
=
=
l
l
; therefore
∆ ′ =
=
y
(
)(
)
.
5
480 633
3 79
mm
mm.
=
Problem
4.
With two slits separated by 0 37
.
mm, the interference pattern has bright fringes with angular spacing 0.065
°
. What is
the wavelength of the light illuminating the slits?
Solution
For small angles, the interference fringes are evenly spaced, with
∆
q
l
=
=
d
(see Equation 371a). Thus,
l
p
=
°
°
=
(
.
)(
.
)(
)
0 37
0 065
180
420
mm
nm.
=
Problem
5.
The green line of gaseous mercury at 546 nm falls on a doubleslit apparatus. If the fifth dark fringe is at 0.113
°
from
the centerline, what is the slit separation?
Solution
The interference minima fall at angles given by Equation 371b; therefore
d
=
+
=
° =
(
)
sin
. (
) sin
.
4
4 5 546
0113
1
2
l
q
=
=
nm
125
.
mm. (Note that
m
=
0 gives the first dark fringe.)
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CHAPTER 37
869
Problem
6.
What is the angular position
q
of the secondorder bright fringe in a doubleslit system with 1.5
m
m slit spacing if the
light has wavelength (a) 400 nm or (b) 700 nm?
Solution
(a) From Equation 371a,
q
l
m
l
=
=
×
=
°
°
=


sin
(
)
sin
(
.
)
.
,
1
1
2
400
15
32 2
700
m
d
=
=
nm
m
and (b) 69.0
for
nm.
Problem
7.
Light shines on a pair of slits whose spacing is three times the wavelength. Find the locations of the first and second
order bright fringes on a screen 50 cm from the slits.
Hint:
Do Equations 372 apply?
Solution
Since
d
=
3
l
, the angles are not small, and Equations 372 do not apply. The interference maxima occur at angles given by
Equation 371a,
q
l
=
=


sin
(
)
sin
(
),
1
1
3
m
d
m
=
=
so only two orders are present, for values of
m
=
<
°
1
90
and 2 (
).
q
If we
assume that the slit/screen geometry is as shown in Fig. 376, then
y
L
L
m
Lm
m
=
=
=


tan
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 Spring '09
 Miller
 Physics, Diffraction, Light, Wavelength, NM

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