=for timestamp
Mo Jul  3 20:16:51 CEST 2006

=head2 95. Hausaufgabe

=head3 Nachlesen des Spektrums von Hg-Dampf-Lam­pen

M<\frac{\lambda}{\mathrm{nm}} = 579{,}1, 577{,}0, 546{,}1, 491{,}6, 435{,}8,
407{,}8, 404{,}7;>

=head3 Wie viele Maxima gibt es für M<g_1 =
\left(\frac{1000}{\mathrm{mm}}\right)^{-1}> und M<g_2 =
\left(\frac{1000}{\mathrm{cm}}\right)^{-1}>?

M<n \lambda = g \sin\alpha;>

M<\frac{n \lambda}{g} = \sin\alpha \leq 1;>

M<n \leq \frac{g}{\lambda};>

     | 579,1 nm  | 404,7 nm
  ---+-----------+----------
  g₁ |  3  (1,7) |  5  (2,5)
  g₂ | 35 (17,3) | 49 (24,7)

=begin comment

#!/usr/bin/perl

use Math::Trig;

use constant L => 10;
use constant G => 1 * 10**(-6);

for my $n (0..3) {
  for my $lambda (map { $_ * 10**(-9) } 579.1, 404.7) {
    printf "n=%d, lambda=%.1f, alpha=%.3f, a=%2.2f\n",
      $n, $lambda * 10**9,
      $n * $lambda / G > 1 ? 0 : asin($n * $lambda / G),
         $n * $lambda / G > 1 ? 0 : L * tan(asin($n * $lambda / G));
  }
}

__EOF__
n=0, lambda=579.1, alpha=0.000, a=0.00
n=0, lambda=404.7, alpha=0.000, a=0.00
n=1, lambda=579.1, alpha=0.618, a=7.10
n=1, lambda=404.7, alpha=0.417, a=4.43
n=2, lambda=579.1, alpha=0.000, a=0.00
n=2, lambda=404.7, alpha=0.943, a=13.78
n=3, lambda=579.1, alpha=0.000, a=0.00
n=3, lambda=404.7, alpha=0.000, a=0.00

=end comment

(Benötigte Zeit: 49 min)