
12.2.
Slit Spectrometers
e„
313
Fig. 12.8. Flux entering spectrometer entrance pupil. See Eq. (12.2.5).
Assuming 6^ is small we can replace sin 9^ by 6^. Substituting for w, h, and
6^ in terms of the telescope and spectrometer parameters gives
4 4 ^^
(12.2.7)
In this form we see that U is the product of
the
collimator (telescope) area S and
the solid angle Q subtended by the slit at the collimator (or by the slit on the sky).
It is also instructive to write U = nw9^
•
hO^. When written in this form, we
see from the discussion following Eq. (2.2.10) that U/n is the product of two
Lagrange invariants with n = I. Because the Lagrange invarian