
216 OPTICS FOR ENGINEERS
The value at half maximum is obtained when
F sin
2
(
nk
)
= 1, (7.118)
so that
k =
2π
λ
=
2πf
c
= arcsin
1
√
F
. (7.119)
The full width at half maximum (FWHM) is
δf = 2
c
2π
arcsin
1
√
F
. (7.120)
More commonly this result is written in terms of the free spectral range
δf
FSR
=
2
π
arcsin
1
√
F
. (7.121)
If we were to measure a spectrum that consisted of two waves closely spaced in frequency,
we would be able to determine that two frequencies were present if they were sufciently far
apart relative to δf , and we would see them as a single wavelength if not. The wavelength
difference at which it is just possible to distinguish the two would depend on