benavides (jjb2356) – homework 41 – Turner – (59130)
1
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001
10.0 points
A heliumneon laser (wavelength 393 nm) is
used to calibrate a diffraction grating.
If the firstorder maximum occurs at 30
.
6
◦
,
what is the line spacing?
Correct answer: 7
.
72039
×
10
−
7
m.
Explanation:
We use the formula
d
sin
θ
=
mλ
for
m
= 1, and obtain
d
=
λ
sin
θ
=
393 nm
sin(30
.
6
◦
)
=
393 nm
0
.
509042
= 7
.
72039
×
10
−
7
m
.
002
(part 1 of 2) 10.0 points
A diffraction grating is 6
.
66 cm long and con
tains 7150 lines per 2
.
39 cm interval.
What is the resolving power of this grating
in the third order?
Correct answer: 59772
.
8.
Explanation:
Let :
L
= 6
.
66 cm
,
N
= 7150 lines
,
and
a
= 2
.
39 cm
.
The diffraction grating’s line density is
n
=
N
a
=
(7150 lines)
(2
.
39 cm)
= 2991
.
63 lines
/
cm
.
Applying the formula for the resolving power
R
of the grating,
R
=
N m
=
n L m ,
where
m
is the order of the diffraction,
N
=
n L
is the number of the illuminated lines of
the diffraction grating, and
L
is the length of
the diffraction grating, we obtain that for the
third order (
m
= 3) the resolving power
R
3
of
the grating is
R
3
=
n L m
= (2991
.
63 lines
/
cm) (6
.
66 cm) (3)
=
59772
.
8
.
003
(part 2 of 2) 10.0 points
If two monochromatic waves incident on this
grating have a mean wavelength of 696 nm,
what is their wavelength separation if they
are just resolved in the third order?
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 Spring '08
 Turner
 Work, Light, 7 m, 6.66 cm, 0.0116441 nm, 393 nm

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