The commissioner shall issue, upon payment of a five-dollar fee, to the owner of ten or more acres of private land or a resident of this state, who has the consent of the owner of ten or more acres of private land, a private land revolver permit that allows the use of a revolver, as defined in section 29-27, to hunt deer from November first to December thirty-first, inclusive, pursuant to the bag limit established for a private land deer permit under subsection (a) of section 26-86a. Any person authorized to hunt deer by revolver pursuant to this section shall use a cartridge of .357 caliber or larger for such purpose.