where i is the angle from the initial plane of polarization to the optic axis of the lamina, s is the angle from the initial plane of polarization to the plane of polarization of the final ordinary image, and ϕ ϕ is the phase lag of the extraordinary wave relative to the ordinary wave due to the difference in propagation times through the lamina. The terms in ϕ ϕ are the frequency-dependent terms and explain why the lamina must be thin in order to produce discernible colors: if the lamina is too thick, cos ⁡ ⁡ ϕ ϕ will pass through too many cycles as the frequency varies through the visible range, and the eye (which divides the visible spectrum into only three bands) will not be able to resolve the cycles.