Atmospheric Ice Optics: 22° Halos, Sun Dogs & Polarized Extinction Dynamics

Atmospheric ice crystals freeze into regular hexagonal prism geometry with prism face angles of $60^\circ$ (between alternating side faces) and $90^\circ$ (between the basal end face and side faces).

When parallel sunlight enters one side face of a randomly oriented hexagonal crystal and exits through an alternating face, the angle of deviation ($\theta$) is governed by Snell's Law. The angle of minimum deviation ($\theta_{\text{min}}$) for an ice refractive index of $n_{\text{ice}} = 1.309$ is:

$$\sin\left(\frac{\theta_{\text{min}} + A}{2}\right) = n_{\text{ice}} \sin\left(\frac{A}{2}\right) \implies \theta_{\text{min}} \approx 21.8^\circ \approx 22^\circ$$

Because rays concentrate heavily at this minimum deviation boundary, an observer on the ground sees a brilliant ring of light with a sharp internal radius of precisely 22 degrees around the sun!

When light refracts and internally reflects within ice crystals, Fresnel equations dictate that the emerging refracted rays are tangentially polarized along the circular perimeter of the halo.

When an observer views a 22° halo while wearing standard linearly polarized sunglasses (which feature a vertical transmission axis to block horizontal ground glare):

• The top and bottom segments of the halo (where polarization is horizontal) are extinguished via Malus's Law ($I = I_0 \cos^2 \theta$), causing them to vanish!
• The lateral sides of the halo (and the sun dogs / parhelia) remain vibrantly visible because their polarization aligns vertically with the glasses.
• Tilting your head by $90^\circ$ causes the lateral sun dogs to disappear while the top and bottom arcs suddenly illuminate!

Mountaineers must understand this trade-off:

1. Polarized Alpine Lenses: Excellent for eliminating blinding horizontal glare from flat snowfields and frozen lake surfaces.
2. Non-Polarized Category 4 Lenses: Strongly preferred by high-altitude expedition climbers when they need to spot treacherous blue ice patches (which rely on specular reflective sheen) or read polarized aircraft and GPS navigation screens.