Astronomy Principles and Practice Fourth Edition.pdf

446 Practical projects
Figure 24.30. The production of a spectrum by using a replica transmission grating.
The optical system is similar to that used for objective prism spectra but differs in that the objective
prism is replaced by an objective grating. With the usual commercially available gratings, the spacing
of the ruling is such that the angular deviation of the spectrum is too great for it to be accepted by
a conventional telescope. The field of view of a 35 mm camera normally allows the spectrum to be
recorded. Consider a typical replica rating (see figure 24.30).
Such a grating may have 500 lines per mm, giving a ruling space of 1/500 mm. By
equation (19.13), the deviation of the first-order spectrum is given by
sin θ = λ d .
Thus, at a wavelength of 5000 Å, the deviation is given by
θ = sin −1 (5000 × 10 −7 × 500)
= sin −1 (0·25)
= 15 ◦ .
A camera providing a field of a little wider than 30 ◦ would, therefore, be able to record most of
the visible first-order solar spectra on either side of normal incidence. If the camera has a smaller field,
it should be set at an angle to the Sun so that the angle of incidence on the grating is not normal.
Now the resolving power of a diffraction grating is given by
R = Nm
where N is the number of lines used on the grating and m is the order of interference. By assuming
that the grating used is 20 mm long and that the first-order spectrum is recorded, the resulting power is