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Alternative idea: the spherical dome has radius of curvature 50 m, and the exposed optical surface is spherical. A ray entering normally from center hits the curved surface at distance d from center, but ray path is straight inside.
But if the surface is curved, then rays not parallel.
But the problem says curves after passing — likely meaning refraction causes beam bending.
Best interpretation: the dome acts as a plano-convex lens with R = 50 m, and the object is at the surface center. Find focal length.
But object at surface center — for plano-convex, if object at surface, f is at surface.
Assume: the curved surface has radius 50 m, and the lens has focal length f.
Wait — focal spot 200 m beyond the center — center is geometric center of hemisphere.
The surface is 50 m from center (since dome radius 50 m).
For a spherical surface, the lensmakers formula:
But perhaps in space habitat optics, typical index 1.5.