Focus offsets for a filter of thickness t can be calculated as follows:
Consider the light from a converging beam falling on a translucent plate of thickness t and refractive index n as shown in Figure .
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Figure: The light path of INT or WHT prime focus near the filter
Now the change in focus
For the glass broad-band filters, the refractive index is 1.6, so the focus offset = 0.38
For the interference filters, the values for the refractive indices are approximately 1.45 for the OII(3727Å), SII(4070Å), HeII, H, OIII, HeI(5876Å), OI and NII filters, and 1.48 for the H, SII(6724Å), OII(7325Å), SIII(9069Å and 9532Å) and HeI(10830Å) filters. (N.B. Do not use the refractive index of the interference coating, which, although of large refractive index (2.1), is thin and enclosed in a glass substrate.
In practise you have to multiply the correction calulated above by (f/f'), where f is the focal length without corrector lens, and f' the focal length of the whole system. For INT prime these values are 2.94 and 3.29, and the change in focus is . For WHT prime these values are 2.498 and 2.81, and the change in focus is .