A magnetometer is provided for detecting a magnetic field of strength B using the Faraday effect. The magnetometer includes a photon emitter, a first polarizer, a prism, a second polarizer, a detector and an analyzer. The emitter projects an emitted light beam substantially parallel to the magnetic field and having wavelength λ. The prism has an interface surface and is composed of a Faraday medium having Verdet value V. The emitted light beam passes through the first polarizer and then the prism, exiting from the interface surface making an incident angle θ0 to normal of the surface and then refracting into a secondary medium as first and second circularly polarized light beams that are separated by a small angular divergence δ. These polarized light beams have average refraction angle θ to the normal and pass through a post-selection polarizer before the detector measures a weak value Aw of a photon having “which path” operator  associated with the polarized light beams. The magnetic field strength is determined as B ≈ - 2 ⁢ ɛ ⁢ ⁢ A w ⁢ π ⁢ ⁢ n 0 ⁢ cos ⁢ ⁢ θ V ⁢ ⁢ λsin ⁢ ⁢ θ 0 . The parameters include n0 as index of refraction of the secondary medium, and ε as amplification factor. The pointer rotation angle Aw can be expressed as A w = ( θ + - θ - ) ⁢ cos ⁢ ⁢ ɛ + [ ( θ + + θ - ) - 2 ⁢ θ 0 ] ⁢ sin ⁢ ⁢ ɛ 2 ⁢ ⁢ sin ⁢ ⁢ ɛ in which θ+ and θ− are respectively right- and left-polarized refraction angles with the average refraction angle such that θ = 1 2 ⁢ ( θ + + θ - ) . The pointer rotation angle Aw can be approximated as Aw≈δ/2ε when 0