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Does depth of field really extend 2/3 behind the subject and 1/3 in front?

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Does depth of field really extend 2/3 behind the subject and 1/3 in front?

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This often cited rule of thumb cannot possibly be right in general, as a simple thought experiment proves: When you have focused your lens at the hyperfocal distance, depth of field extends infinitely far back. If the 2/3 rule were true, then depth of field would need to extend infinitely far in front as well (since 1/3 of infinity is still infinity), and objects behind the camera would need to be in focus. This is obviously ridiculous, so the 2/3 rule cannot be right in general.

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