# Can a single optical device converge as well as diverge a parallel beam of light?

A biconvex lens converges a parallel beam of light when the beam is incident on either of its convex surfaces. A biconcave lens diverges a parallel beam of light when the beam is incident on either of its concave surfaces. Similarly, plano convex and plano concave lenses converge or diverge a parallel beam irrespective of whether the plane side or the curved side faces the beam.

It can be seen that when the medium in which the lens is placed is uniform throughout, and if the lens converges or diverges a parallel beam of light when one of its side faces the beam, then, when the other side faces the beam it behaves in a similar manner, although the focal length may vary which may depend on the curvature of the two sides. The sign of the focal length determines whether the lens behaves as a converging or a diverging device. When it's positive, the lens converges a parallel beam and when it's negative, the lens diverges the beam.

Is it possible for an optical device (consisting of lens(es)) to converge as well as diverge a parallel beam of light when the beam is incident on its two different sides? Alternatively, can the focal length of an optical device have two different signs when measured along different sides? If an optical device converges a parallel beam of light when the beam is incident on one side, does it imply when the beam is incident on the other side, the beam converges again?

I've constructed the following diagrams to make my question clearer. In the following images, the blue coloured dotted rectangle represents an optical device. It's orientation is marked using the two fat red arrows at the top and the bottom of the rectangle. The optical centre is assumed to be at the geometric centre of the rectangle. A parallel beam of light is incident from the left side. If the optical device converges the beam as shown in the first diagram below: Is it possible for the same optical device to diverge the parallel beam when it's rotated so that the other side faces the beam, as shown in the following diagram?: I'm unable to think of any such optical devices (lenses or combination of lenses). I also tried various combination of lenses using this Phet simulation. But in all cases when a device converges from one side, it behaves in the same way when the beam is incident on the other side.

Image credit : My own work :)