Photon trapping curve

Question

Is there a closed smooth planar curve and a direction satisfying the following property?

The closed smooth curve separates the plane into two disconnected domains, one interior the other exterior. Cut a finite connected segment, called opening, out of the curve. "Shoot" a "photon" through the opening into the interior in the aforementioned direction. The photon bounces off of the curve with the same angle as the incident line with respect to the normal vector of the curve. The photon will remain trapped inside the interior after traversing an infinitely long distance.

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An extension the question is here.

Answer 1

It is possible to make such a curve for which a particular ray of light will keep bouncing back and forth within a confined region even if the curve is not closed.

One specific case is a hyperbola, but I'm sure there are other examples.

The hyperbola has a reflective property, like the other conic sections. If a ray of light is aimed at one focus, the reflection of that ray will be heading towards the other focus. This will then be reflected back and forth indefinitely.

All you need to make a concrete example are the two segments of the hyperbola around the x-axis, and then fill in the rest with anything that does not block the rays.

And, yes, I stole the illustration from the reference I gave as I'm no good at making them. If my answer is not clear enough, I can try making a better drawing.

Answer 2

Inspired by Einar Røland's answer, I found the ellipse works as well. The ellipse has the same reflection property as the hyperbola, namely, the light ray emanating from one focal point will be reflected by the boundary back towards the other focal point. A light ray shot in from a small aperture on the boundary sufficiently away from its intersection with the major axis towards one focal point will converge to the major axis and trapped in the vicinity.