Calculate lens diameter using NA

[Lanc1988]

Homework Statement

A projection aligner has an object to lens distance of 500mm. Calculate lens diameter for the aligner if NA = 0.28. Assume the usable area of lens is 90% of its diameter.

Homework Equations

NA = r / D
Note: NA is the numerical aperture.

The Attempt at a Solution

I know that NA = r / D which means 0.28 = r / 500 and then r = 140mm so the diameter of the lens would be 280mm but I'm unsure how to use the idea of 90% of the lens being usable.

 

[darkys]

It seems that the answer would still be 280mm but I'm not completely sure. Any help would be appreciated. Thanks.