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There are two competitive opinions about a magnitude of the momentum of light in matter. The Balazs thought experiment gives unambiguous theoretical evidence based only on laws of mechanics that the momentum of light in matter is smaller by n times than that of the same light in free space where n is the refractive index of the matter. On the other hand, there is other theoretical evidence confirmed by experimental investigation that the momentum of light in matter is greater by n times than that in free space. This ancient dilemma cannot be resolved till now. We show that the momentum density flux of light in matter is greater by n times than that in free space. In the same time we present an alternative interpretation of the Balazs thought experiment where two optical pressures arising in the regions of the matter where leading and trailing edges of the pulse are propagating are taken into account. This enables us to match contradictory results of mentioned experiments. Since the contradiction is overcome, the dilemma disappears

Resolution of the Age-Old Dilemma about a Magnitude of the Momentum of Light in Matter