Why a 1 mW Helium-Neon Laser
Still Appears Bright a Mile Away
At a distance of 1 mile (1,609 m), the beam from a typical
helium-neon laser (which is a quite well collimated
source) will have spread to a diameter of roughly 4
feet (48 inches, 1.3 m). However, it will still appear
quite bright. Why is this so?
The fraction of light entering the eye for a large
diameter beam is pupil area divided by beam area.
Assuming a pupil diameter of 1/4 inch (6.3 mm, rather
dilated but not fully dark adapted which may approach
1 cm). The portion of the beam entering the eye would
then be the square of (1/4)/(48), which is about 27
millionths of the total. Since the 4 foot diameter beam
is not uniform but dimmer towards the edges, I would
say the eye could get about 35 millionths of the beam
near the center or 35 nanowatts (35 nW).
Note that close to the laser, the pupil size is going
to be larger than the beam diameter (which is typically
less than 1 mm) and pupil size larger than this will
not affect the maximum possible power entering the eye
(though it will affect the probability of this occurring.
(One suggested laser safety practice is to brightly
illuminate the laser lab to make your pupils smaller.
Even though there are times this will not reduce the
severity of the worst case, a smaller target reduces
likelihood of this happening.)
However, where the beam diameter is equal to or larger
than the pupil diameter, the difference in pupil diameter
between bright and dark adapted eyes will be very significant
- more than a 30-fold difference in power entering the
eye for this analysis.
We calculate that a 4 foot diameter 1 mW 632.8 nM beam
appears about as bright as a 100 W bulb does 88 feet
away.
Although 35 nW is definitely eye-safe, it may look
quite bright against pitch black surroundings especially
when the eye is fully dark adapted (the pupil is wide
open and the combined retinal/neural sensitivity is
maximum as it is after awhile when out at night) and
may quickly result in a noticeable afterimage. The effect
is probably enhanced by the knowledge that the light
source is a laser and thus potentially damaging to your
eyesight.
As a side note, the 1,710 lumen output of a typical
100 Watt incandescent bulb is about the same lumens
as *10 Watts* of 632.8 nm light!
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