The "twilight factor"was explained to me many years ago by a gunsmith and seems to make sense. Sometimes the twilight figure was expressed in the nomenclature of the scope. Example - remember the Pecar 4x scopes that were very popular in the 1960's/70's? They were designated 4x81 and obviously didn't have an 81mm objective. The figure of 81 is derived from the actual scope exit pupil of 9 which is then squared (9x9=81). The real objective diameter of the Pecar was 36mm (4x9=36).
Similarly, some lower end Japanese brands fixed 4x scopes were advertised as having a twilight figure of 100. These had a 40mm objective - thus 40 divided by 4 gives an exit pupil of 10 and 10 squared (10x10) is 100. You never saw higher grade fixed 4x scopes such as the European and U.S. brands have 40mm objectives as the human eye can't use an exit pupil of 10mm so the larger objective was unnecessary.
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