Physics Photo of the Week
Parhelia and Ice Halo
November 10, 2010, a broad array of cirrus clouds created the ice
halo that almost completely surrounds the Sun. In addition the
clouds created bright, colorful parhelia -
the bright spots at almost the same elevation as the Sun but a bit
further away from the Sun than the halo. Both the halo and the
parhelia are caused by the prism effects of millions of ice crystals
that make up the cirrus clouds. Whenever I notice cirrus clouds I
automatically look for haloes.
(Compare this phenomenon with the circumzenithal arc that was
featured on PPOW
Nov. 12, 2010).
The presence of the halo indicates the presence of hexagonal
needle-like ice crystals (like hexagonal pencils) in the cirrus
clouds. The parahelia indicate the presence of flat plate
hexagonal ice crystals. Thus the ice cloud phenomenon here
indicates the presence of both hexagonal needles and hexagonal plates.
How do randomly-oriented ice crystals produce a coherent halo?
The answer depends on two physics phenomena. One, the orientation
is not completely random. The ice crystals are falling with a
constant velocity in the air on account of gravity and air friction
(witness snowflakes falling). The orientation is stable only if
the needles are horizontal. Note how flat leaves tend to float
downward swooshing back and forth in a horizontal orientation. As
a general rule, things falling in air orient themselves such that the
largest dimension is horizontal. Yes, it's counter-intuitive!
Even though the needle-like ice crystals are horizontal due to air
friction, they can still have a random rotation about the long axis and
a random horizontal orientation, but they are all horizontal. The
drawing below shows the hexagonal needles in cross-section
several different rotations about the long axis. These act as
The optical properties of the hexagons are identical to
that of equalatorial triangles. Hexagons
merely triangles with the points truncated. The green line
represents sunlight entering the prisms. The three
drawings represent the prisms for three different orientations relative
to the sunlight. The deflections of the sunlight are the result
of refraction of light following the laws of optical refraction.
The deflection angle for the light beam is indicated by the angle
D. The deflection angle is smallest for the orientation of the
crystal on the left, where the path is symmetric. If the crystal
is rotated clockwise or counter-clockwise from the symmetric position,
the deflection angle increases as shown in the drawings. The
minimum deflection angle for the ice crystals is 22 degrees.
In the cirrus clouds made of the hexagonal crystals, the crystals are
all horizontal, but they exhibit random directional orientations and
random rotations about their long axes. For different
orientations about the long axes, the crystals will deflect the light
at least as large as the minimum deflection of 22 degrees as in the
diagram above. Thus in the sky the sunlight through the crystals
will brighten the sky at an angle greater than 22 degrees from the
Sun. At 22 degrees, the deflected light will be enhanced the
most. Because the needles are directionally oriented at many
angles (North, East, South, West, etc) the deflection of the Sun's rays
forms a ring around the Sun (the 22 degree halo). Some color is
produced because the refractive index for ice (and all transparent
materials) depends on the color. Thus the minimum deflection is
slightly different for the different colors - causing the separation of
white light into the component colors.
The optics of the parhelia will be discussed in a future PPOW.
Photo of the
published weekly during the academic year on Fridays by the Warren
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