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To be optically active the presence of chiral centres are very important but if there exists a plane centre or axis of symmetry then the molecules are optically inactive. How to determine the optical activity when more than one ring are present? Is it sufficient to check those two mentioned condition?

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    $\begingroup$ Rings are irrelevant. The rules for many rings are the same as with one ring or without rings at all. Besides, symmetry axes are also irrelevant. $\endgroup$
    – Ivan Neretin
    Commented Mar 8, 2018 at 14:32

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How to determine the optical activity when more than one ring are present? Is it sufficient to check those two mentioned condition?

As Ivan Neretin accurately noted above:

  • the rules for determining optical activity of a molecule are the same for all molecules, whether it has one ring, several rings, or no rings at all.
  • axes of symmetry are irrelevant in determining the optical activity of a molecule. We only have to consider center and plane of symmetry.

That said, the given molecules have several chiral centers, which is a great sign that the molecule may be optically active.

If you will try to find the plane of symmetry, you won't find any. While the rings may appear planar on the paper, they (even the fused ones) actually exist as conformations in 3D.

Moreover, the center of symmetry is a point that requires identical groups equidistant from itself; a quick glance over both the molecules shows there are no such centers.

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