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Matching scope with camera chip size


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If I use my ultrastar , 0.5 reducer with my C11 then vignetting is obvious, Thus I assume at this F ratio of F5 then the chip is not fully illuminated. If I use the f6.3 reducer there is no vignetting. 

My question - is there a general formula to work out F ratio to chip size such that there is no vignetting (or minimal).

I would like to try different cameras but do not wish to buy one that has the wrong chip size.

Thanks, Mike

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