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54. We are given the “number of lines per millimeter” (which is a common way to
express 1/
d
for diffraction gratings); thus,
1
d
=
160
lines/mm
⇒
d
= 6.25
×
10
−
6
m .
(a) We solve Eq. 3625 for
θ
with various values of
m
and
λ.
We show here the
m =
2
and
λ
= 460 nm calculation:
()
9
11
1
6
10 m)
sin
sin
sin
0.1472
8.46 .
6.25 10 m
m
d
λ
−
−−
−
−
⎛⎞
2(460×
==
=
=
°
⎜⎟
×
⎝⎠
Similarly, we get 11.81° for
m =
2 and
λ
= 640 nm, 12.75° for
m =
3 and
λ
= 460 nm,
and 17.89° for
m =
3 and
λ
= 640 nm.
The first indication of overlap occurs when we
compute the angle for
m =
4 and
λ
= 460 nm; the result is 17.12° which clearly shows
overlap with the largewavelength portion of the
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 Spring '08
 Any
 Physics, Diffraction

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