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Added "quickly" because if slowly, then maybe would diverge.
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Joseph O'Rourke
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Just empirically, I believe the OP's $e^{-x}$ example has the property that ray reflections quickly become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)

Just empirically, I believe the OP's $e^{-x}$ example has the property that ray reflections become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)

Just empirically, I believe the OP's $e^{-x}$ example has the property that ray reflections quickly become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)
added 9 characters in body
Source Link
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

Just empirically, I believe the OP's $e^{-x}$ example has the property that ray reflections become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)

Just empirically, I believe the OP's example has the property that ray reflections become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)

Just empirically, I believe the OP's $e^{-x}$ example has the property that ray reflections become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)
Source Link
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

Just empirically, I believe the OP's example has the property that ray reflections become increasingly vertical, and so will not reach arbitrarily large $x$:


          ![exconvex][1]
(I did not, however, perform the calculations to prove this.)