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The hyperbolic reflector in equation A-1 becomes a plane
dipping reflector when
. In this case, equation A-5
simplifies to (Klokov and Fomel, 2012)
![\begin{displaymath}
t_m(x_m) = \frac{2}{v} \frac{(x_m-x_0) \cos{\alpha} \sin{\beta}}{1-\gamma \sin{\alpha} \sin{\beta}}\;.
\end{displaymath}](img60.png) |
(21) |
The dip of the image at a correct velocity is
![\begin{displaymath}
\tan{\alpha_m} = \frac{v}{2} t_m'(x_m) = \frac{\cos{\alpha} \sin{\beta}}{1-\sin{\alpha} \sin{\beta}}\;,
\end{displaymath}](img61.png) |
(22) |
which is equivalent to equation 8 in the main text. The dip of the reflector in this case is simply
. It
is easy to verify that when
,
.
2014-03-25