Based on the new results of studying extraordinary rays′ behavior and the refractive index of the extraordinary wave in uniaxial crystal , an exact model of the optical path difference yielded by birefringent filters is set up. Then the versatile and precise formula for the filters is derived without the approximation Δn=n o-n e≤n o (or n e). The new model shows the correct position and dimension in each path while the filter is tuning. The formula is applicable not only to the filter made of the crystal with the optical axis parallel to the surface (FAPS) also to the one with the axis incline to the surface (FAIS). It is pointed out that the FAIS enables to tune laser wavelengths in a wider range than the FAPS. The origin of the wide range is interpreted as the variation in the index of the FAIS is larger while tuning the filter. With the help of the formula, a FAIS for tuning a Ti:sapphire laser is presented.