Physics Photo of the Week

December 3, 2010

Parhelia and Ice Halo
On 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 for 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 for several different rotations about the long axis.  These act as prisms.  The optical properties of the hexagons are identical to that of equalatorial trianglesHexagons are 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.

Physics Photo of the Week is published weekly during the academic year on Fridays by the Warren Wilson College Physics Department.  These photos feature interesting phenomena in the world around us.  Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation.  Atmospheric phenomena are especially welcome.  Please send any photos to dcollins@warren-wilson.edu.

All photos and discussions are copyright by Donald Collins or by the person credited for the photo and/or discussion.  These photos and discussions may be used for private individual use or educational use.  Any commercial use without written permission of the photoprovider is forbidden.