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A good rule of thumb is to make the secondary about 25-30% of the aperture. Using this as a guide the 38mm size is the most appropriate.
Another way is to check the focal length and where you want the eyepiece. The ratio of the path to the mirror and the mirror to the eyepiece is the key to ensuring the mirror is fully illuminated.
If the scope is a F9 6" The total focal length is 54". From the centre of the OTA to the focal plane will be about 8" allowing for the focusing mechanism thus the secondary mirror will be about 46" from the primary making the ratio about 6:1. So the secondary will need to be at least 1" if it can be positioned precisely but to ensure that all the light is captured the optimum size will need to be nearer to double this.
Barry
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