We describe a tunable bandpass filter and polarizer based on resonant tunneling through an air gap between two hemi-cylindrical prisms coated with 4-layer a-Si/SiO2 matching stacks. Tuning is achieved by simultaneous variations in the incident angle and the air gap thickness, enabling the pass-band center wavelength to be continuously adjusted over a very wide range (potentially ~1000 - 1800 nm) with an approximately fixed fractional bandwidth (Δλ/λ ~1%). An analytical derivation of the conditions required to produce a flat-top TE pass-band at a desired wavelength is given. The filter provides excellent out-of-band rejection and strong suppression of the orthogonal TM polarization over the entire tuning range. For applications involving collimated light, it could be a useful alternative to existing widely tunable filters based on gratings or liquid crystals.