Calculate lens diameter using NA

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To calculate the lens diameter for a projection aligner with an object to lens distance of 500mm and a numerical aperture (NA) of 0.28, the formula NA = r / D is applied. This results in a calculated radius (r) of 140mm, leading to a total diameter (D) of 280mm. However, considering that only 90% of the lens area is usable, the effective diameter may need to be adjusted. The user expresses uncertainty about how to incorporate the 90% usability factor into the final diameter calculation. Clarification on this aspect is sought to ensure the correct lens diameter is determined.
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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.
 
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It seems that the answer would still be 280mm but I'm not completely sure. Any help would be appreciated. Thanks.
 

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