Utilising the filter in uncollimated (i.e. convergent or divergent) light involves slightly more complex considerations. Here, light enters the filter at a range of angles, so that different rays undergo unequal wavelength shifts. This results in not only a central wavelength shift, but a broadening of the bandwidth and lower peak transmission.
As a rough approximation, relatively uniform beams (with full cone angles less than 20 ) will undergo peak shifts of approximately one half of that which would be predicted for a collimated beam at the maximum angle of incidence of the cone.
The filters were specified for a focal ratio of 4.5, having a maximum angle of incidence of the cone of , and of effective refractive index 1.6.
Substituting these values in the equation,
The focal ratio of the WHT prime focus is 2.8, which gives a maximum angle of incidence of the cone of , so, substituting again into the equation,
Therefore, at the WHT prime focus, the central wavelength (i.e. the wavelength of peak transmission) is shifted towards shorter wavelengths by 0.15% from the specified central wavelengths. For example, for an filter with specified central wavelength 6560Å, the effective central wavelength will be 6550Å.