As an advocate of dim-light binoculars for hunters, years ago I developed and published in
Safari magazine a formula for gauging optics performance in dim light, based on
magnification and objective lens size. It works equally well for binoculars, spotting scopes
and rifle scopes.
The standard American formula is called Relative Brightness; it’s basically the width of the exit
pupil squared. (Hold your binoculars or other optic at arms length and look into the ocular
(eyepiece) lens; the solid circle of light you see is the exit pupil.) The exit pupil is defined
by magnification and objective lens width in millimeters - divide the objective lens width by
the magnification and you have your exit pupil width, as follows:
3 x 18 [opera glass] - Exit Pupil, 6 millimeters
7 x 35 - Exit Pupil, 5 millimeters
7 x 42 - Exit Pupil, 6 millimeters
7 x 50 - Exit Pupil, 7.14 millimeters
8 x 30 - Exit Pupil, 3.75 millimeters
8 x 56 - Exit Pupil, 7 millimeters
10 x 40 - Exit Pupil, 4 millimeters
20 x 50 - Exit Pupil, 2.5 millimeters
That makes the Relative Brightness ratings for these optics as follows:
3 x 18 [opera glass] - 36
7 x 35 - 25
7 x 42 - 36
7 x 50 - 50.9
8 x 30 - 14
8 x 56 - 49
10 x 40 - 16
20 x 50 - 6.25
The long-established formula popular in Europe is called Twilight Factor, which is the square
root of the magnification multiplied by the objective lens width in millimeters. The Twilight
Factor for the same optics are as follows:
3 x 18 [opera glass] - 7.34
7 x 35 - 15.65
7 x 42 - 17.14
7 x 50 - 18.7
8 x 30 - 15.49
8 x 56 - 21.16
10 x 40 - 20
20 x 50 - 31.6
If you start comparing ratings - Relative Brightness vs. Twilight Factor - problems arise.
According to Relative Brightness, the little opera glasses, with an RB of 36, are over twice
as effective in dim light as a pair of 10 x 40s. This is nonsense, of course. Twilight Factor,
on the other hand, shows a 20 x 50 spotting scope with a TF of 31.6 to be far brighter than
a 7x50 naval binocular, which is equally absurd. The trouble is that Relative Brightness
places too much emphasis on exit pupil size, and Twilight Factor on magnification.
I dubbed my solution Effective Brightness and it isn’t complicated: just take the average of
a given optic’s Relative Brightness and Twilight Factor ratings. Basically, it tames the extremes.
Under Effective Brightness, we end up with the following ratings:
3 x 18 [opera glass] - 21.67
7 x 35 - 20.32
7 x 42 - 26.57
7 x 50 - 34.8
8 x 30 - 14.74
8 x 56 - 35.08
10 x 40 - 18.00
20 x 50 - 18.92
Perfect, it isn’t; few formulas are. But after a lot of dusk-and-dawn testing, I found it to be
far more accurate than Relative Brightness or Twilight Factor. To determine your variable rifle
scope’s best dim-light setting, calculate what will give you a 7mm exit pupil and you’’re
there. (In my Zeiss 1.5-6 x 42, for instance, that means 6x. The reason for this is that by
and large the human pupil generally cannot open any wider than 7 millimeters - especially
for those of us who aren’t 18 anymore - so anything wider than a 7mm exit pupil is
wasted, in terms of dim-light performance.
To give it a test run yourself, pick up a newspaper or large magazine with varying sizes of
headline or front-page print (or, ideally, an optometrist’s eyeglass chart) and set it up at a
specific range, say 100 yards. (Or whatever range you can clearly make out the headlines
or front-page print in broad daylight.) Then set up at that identical distance as it begins to
get dark in the evening and keep track of the latest time you can still read the same
letters. (Reverse the process for pre-dawn and dawn tests.) Compare your results with
different configurations - an 8 x 30 against a 7 x 42, for instance - and you’’ll see the
difference. Bottom line? A dim-light glass (my definition: 7 x 42, 7 x 50, or 8 x 56) can get
you onto game as much as 30 minutes earlier or later than a smaller glass. Heavier? No
doubt about it, but what you gain can make a big difference, even during long glassing
sessions during the day: because of the large exit pupil, you’’re less apt to experience eye strain.
The other thing, of course, is that the formula assumes equal quality among optics, which
can be very misleading. A pair of $25 Wal-Mart 7 x 35s are not going to perform better in
dim light than a set of 8 x 30 Swarovskis, regardless of what any formula says. But used
among optics of equal quality, the numbers tend to hold true.
Many of us are just not disposed to carry heavier binoculars; in any event, my philosophy
has always been the carry the highest Effective Brightness glasses you're willing to pack.
Dick Blust, Jr.
Rock Springs, Wyoming
