A　quantitative　understanding　about　the　optical　scattering　of　medium　plays　an　important　role　in　many　common　but　important　application　fields　including　optical　imaging,　optical　communication,　and　optical　remote　sensing.　In　this　paper,　two　quantitative　models　about　single　scattering　and　multiple　scattering　were　established　based　on　the　different　polarization　properties　of　these　two　scattering　processes　on　the　condition　of　paraxial　approximation.　The　related　approximate　explicit　functions　about　the　light　scattering　characteristics　through　fog　are　solved.　Moreover,　on　the　basis　of　scattering　models,　the　depolarization　ratio　of　broad-band　polarized　light　is　also　measured.　The　physical　models　are　demonstrated　very　consistent　with　the　experimental　results　and　Monte　Carlo　simulations.　These　works　greatly　simplify　previous　models　and　have　a　significant　promotion　to　the　study　of　medium　scattering　characteristics.　(c)　2022　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement