Fig. 5.28.
5.141. With light falling normally on a transparent diffraction
grating 10 mm wide, it was found that the components of the yellow
line of sodium (589.0 and 589.6 nm) are resolved beginning with
the fifth order of the spectrum. Evaluate:
(a)
the period of this grating;
(b)
what must be the width of the grating with the same period
for a doublet k = 460.0 nm whose components differ by 0.13 nm
to be resolved in the third order of the spectrum.
5.142. A transparent diffraction grating of a quartz spectrograph
is 25 mm wide and has 250 lines per millimetre. The focal length
of an objective in whose focal plane a photographic plate is located
is equal to 80 cm. Light falls on the grating at right angles. The
spectrum under investigation includes a doublet with components
of wavelengths 310.154 and 310.184 nm. Determine:
(a)
the distances on the photographic plate between the components
of this doublet in the spectra of the first and the second order;
(b)
whether these components will be resolved in these orders
of the spectrum.
5.143. The ultimate resolving power VSX of the spectrograph's
trihedral prism is determined by diffraction of light at the prism
edges (as in the case of a slit). When the prism is oriented to the
least deviation angle in accordance with Rayleigh's criterion,
A,/SA, =
b I dnIcA,
I,
where
b
is the width of the prism's base (Fig. 5.28), and
dnIdk
is the
dispersion of its material. Derive this formula.
5.144. A spectrograph's trihedral prism is manufactured from
glass whose refractive index varies with wavelength as n =
A +
where
A
and
B
are constants, with
B
being equal to 0.010 1.tra
2
.
Making use of the formula from the foregoing problem, find:
(a)
how the resolving power of the prism depends on k; calculate
the value of kin in the vicinity of k
i
= 434 nm and
21,2 =
656 nm
if the width of the prism's base is
b =
5.0 cm;
(b)
the width of the prism's base capable of resolving the yellow
doublet of sodium (589.0 and 589.6 nm).
5.145. How wide is the base of a trihedral prism which has the
same resolving power as a diffraction grating with 10 000 lines
in the second order of the spectrum if I
dn/c/Al
= 0.10 pm--
1
?
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