f number adjustment to increase light level

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I was intrigued by a statement I made during a review of a sample exam
session and this afternoon decided to find out what the new f# should
be given that one wants to increase the light level at the image plane
over that available at some starting f#. After 4 hours of pondering
came up with this (whole increments would be quite easy ...):

http://www.davidhazy.org/andpph/text-fnumber-aperture-adjustment.html

I am sure there are easier ways to do this and if so a hint would be
most welcome! Of course fractional or "decimal" f#s are not easy to set!

Andy



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