Moon Halos.

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Moon Halos. On nights with diffuse high clouds
and a bright moon, a halo can appear about the
moon. This results from light refracting (through
an angle of 22 degrees) through hexagonal ice
crystals in the atmosphere. The mathematics is as
follows
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Hexagonal ice crystals look something like this.
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A side-on view of an ice crystal
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When light strikes the boundary between two
different substances (air and ice) it refracts.
Light ray
Air-Ice boundary
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Snells Law is the physical relation governing
refraction. It states that the angle of incidence
and the angle of refraction are related by the
formula
The constant k depends on the nature of the two
substances. For air-ice, it is about 1.31.
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Light enters the crystal, and then leaves it,
making two refractions.
?1
?2
?
?3
?4
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Here, the angle a represents the total angle the
light bends.
?1
?2
?
?3
?4
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The necessary relations needed to determine a are
on the next slide.
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?1
?2
?
?3
?4
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We solve the relations on the next slide.
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Technically speaking, there are about a zillion
ice crystals in the atmosphere all oriented
randomly. The angle
will take many different values.
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This means that the light will be scattered
through many different angles, though there is a
catch.
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If there are many different angles of incidence
that yield approximately the same a, light will
seem to build up at that angle.
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Light builds up most where the slope is smallest.
This is 21.83929990 degrees.
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This is the classic 22 moon halo.
Moonlight
Diffuse clouds
Apparent Halo
22
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Light inside the halo is refracted out in a cone
that misses the observer, making this region less
bright to the observer.
Moonlight
Diffuse clouds
Apparent Halo
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Light outside the halo is refracted out in a cone
that misses the observer, making this region less
bright to the observer.
Moonlight
Diffuse clouds
Apparent Halo
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Light on the halo is refracted out in a cone that
the observer sees, making this region brighter to
the observer.
Moonlight
Diffuse clouds
Apparent Halo