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Unformatted text preview: 44. At the point on the screen where we ﬁnd the inner edge of the hole, we have tan θ = 5.0 cm/30 cm,
which gives θ = 9.46◦ . We note that d for the grating is equal to 1.0 mm/350 = 1.0 × 106 nm/350. From
mλ = d sin θ, we ﬁnd
1.0×106 nm
(0.1644)
350
d sin θ
470 nm
m=
=
=
.
λ
λ
λ
Since for white light λ > 400 nm, the only integer m allowed here is m = 1. Thus, at one edge of the
hole, λ = 470 nm. However, at the other edge, we have tan θ = 6.0 cm/30 cm, which gives θ = 11.31◦ .
This leads to
1.0 × 106 nm
λ = d sin θ =
sin 11.31◦ = 560 nm .
350
Consequently, the range of wavelength is from 470 to 560 nm. ...
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 Fall '08
 SPRUNGER
 Physics

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