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51. (a) Since the resolving power of a grating is given by
R
=
λ/
∆
λ
and by
Nm
, the range of wavelengths
that can just be resolved in order
m
is ∆
λ
=
λ/Nm
.He
re
N
is the number of rulings in the grating
and
λ
is the average wavelength. The frequency
f
is related to the wavelength by
fλ
=
c
,where
c
is the speed of light. This means
f
∆
λ
+
λ
∆
f
=0,so
∆
λ
=
−
λ
f
∆
f
=
−
λ
2
c
∆
f
where
f
=
c/λ
is used. The negative sign means that an increase in frequency corresponds to a
decrease in wavelength. We may interpret ∆
f
as the range of frequencies that can be resolved and
take it to be positive. Then,
λ
2
c
∆
f
=
λ
Nm
and
∆
f
=
c
Nmλ
.
(b) The diFerence in travel time for waves traveling along the two extreme rays is ∆
t
=∆
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Power

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