We propose a paraxial dual-cone model of conical refraction involving the interference of two cones of light behind the exit face of the crystal. The supporting experiment is based on beam selecting elements breaking down the conically refracted beam into two separate hollow cones which are symmetrical with one another. The shape of these cones of light is a product of a 'competition' between the divergence caused by the conical refraction and the convergence due to the focusing by the lens. The developed mathematical description of the conical refraction demonstrates an excellent agreement with experiment.
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