parenrightbigg
Î» ,
where
m
= 0
,
Â±
1
,
Â±
2
,
Â±
3
,
so for the third
dark fringe (
m
= 2),
Î´
=
parenleftbigg
m
+
1
2
parenrightbigg
Î»
=
5
2
Î»
and
Î´
Î»
=
Ï†
2
Ï€
=
5
2
Ï†
= 5
Ï€ .
006(part2of2)10.0points
Using the small angle approximation (
Î¸
=
sin
Î¸
= tan
Î¸
)
,
if the distance from the central
bright region to the third dark fringe is
y
,
what is the wavelength of the light?
1.
Î»
=
2
7
d y
L
2.
Î»
=
2
5
d L
y
3.
Î»
=
2
5
L y
d
4.
Î»
=
2
7
d L
y
5.
Î»
=
2
5
d y
L
correct
6.
None of these
7.
Î»
=
1
3
d y
L
8.
Î»
=
1
3
d L
y
9.
Î»
=
2
7
L y
d
10.
Î»
=
1
3
L y
d
Explanation:
scribner (eks662) â€“ interference diffraction HW â€“ yeazell â€“ (55745)
3
r
2
r
1
y
L
d
S
1
S
2
Î¸
= tan
âˆ’
1
parenleftBig
y
L
parenrightBig
viewing
screen
Î´
â‰ˆ
d
sin
Î¸
â‰ˆ
r
2

r
1
P
O
negationslash
S
2
Q S
1
â‰ˆ
90
â—¦
Q
r
2
r
1
d
=
h
2
S
1
S
2
Î¸
= tan
âˆ’
1
parenleftBig
y
L
parenrightBig
Î¸
Î´
â‰ˆ
2
h
sin
Î¸
â‰ˆ
r
2

r
1
negationslash
S
2
Q S
1
â‰ˆ
90
â—¦
Q
The angle
Î¸
from the slitsâ€™ midpoint to the
y
position on the screen is
tan
Î¸
=
y
L
â‰ˆ
sin
Î¸ ,
so the wavelength of the light for the third
dark fringe (
m
= 2) is
parenleftbigg
m
+
1
2
parenrightbigg
Î»
=
d
sin
Î¸
5
2
Î»
=
d
y
L
Î»
=
2
5
d y
L
.
007
10.0points
A screen is illuminated by light with wave
length
Î»
as shown. The distance from the slits
to the screen is
L .
y
L
d
S
1
S
2
Î¸
viewing
screen
Using the small angle approximation (
Î¸
=
sin
Î¸
= tan
Î¸
)
,
how far apart
y
is the sixth
dark fringe from the central bright fringe?
1.
y
=
11
2
L d
Î»
2.
y
= 6
d Î»
L
3.
y
= 6
L d
Î»
4.
y
=
13
2
d Î»
L
5.
y
=
11
2
L Î»
d
correct
6.
y
=
13
2
L d
Î»
7.
y
= 6
L Î»
d
8.
y
=
11
2
d Î»
L
9.
y
=
13
2
L Î»
d
10.
None of these
Explanation:
For dark fringes
Î´
=
d
sin
Î¸
=
parenleftbigg
m
+
1
2
parenrightbigg
Î» ,
where
m
= 0
,
Â±
1
,
Â±
2
,
Â±
3
.
L
y
=
11
2
L Î»
d
.
008
10.0points
In a Youngâ€™s doubleslit experiment using
294 nm light, a thin piece of plexiglass of
refractive index 1
.
52 covers one of the slits.
If the center point on the screen is a dark
spot instead of a bright spot, what is the
minimum thickness of the plexiglass?