$$ FWHM = (\frac{a\cdot cos\alpha\cdot w}{k\cdot f}) $$
Where:
The above entries must be sorted in the order in which they appear in the equation from left to right.
Assumptions:
Spectral order is 1
Incident angle of light is 0 degrees
Derivation
https://folk.ntnu.no/torarnj/Design_of_a_Hyperspectral_Imager_Using_COTS_Optics_for_Small_Satellite_Applications.pdf