Deriving Optics: 22/46 Halo, Sundogs, Coronas, etc.

[xreas0nsx]

i have no idea where to start:

can someone help me mathematically derive the following?

-22 degree halo and 46 degree halo

-sundogs

-coronas

-sunrise/ sunset

-silver linings

-sun pillar

(graphics would be greatly appreciated)

if you find any helpful links please cite them here!

thanks!

 

[Andrew Mason]

i have no idea where to start:

can someone help me mathematically derive the following?

-22 degree halo and 46 degree halo

-sundogs

-coronas

-sunrise/ sunset

-silver linings

-sun pillar

(graphics would be greatly appreciated)

if you find any helpful links please cite them here!

thanks!

Check out this http://www.sundog.clara.co.uk/halo/parhelia.htm" which has great photos and a fairly good explanation.

AM

 

[kyle8921]

I would be happy to help you with deriving these optical phenomena mathematically. However, it is important to note that while we can understand and explain these phenomena using mathematical equations, their occurrence is ultimately dependent on various atmospheric conditions and the properties of light. With that in mind, let's take a look at each of these phenomena individually:

22 degree halo and 46 degree halo:

To derive the 22 degree halo and 46 degree halo, we need to understand the concept of refraction and the geometry of light passing through ice crystals in the atmosphere. The halo is formed when light from the sun or moon is refracted (bent) by hexagonal ice crystals in the atmosphere, producing a ring of light around the sun or moon. This refraction occurs at an angle of 22 degrees for the inner ring and 46 degrees for the outer ring.

To derive these angles, we can use Snell's Law, which states that the angle of refraction is related to the angle of incidence and the refractive index of the medium. In this case, the medium is the ice crystals in the atmosphere. We can also use the geometry of a hexagonal crystal to calculate the angles at which light is refracted. This website provides a detailed explanation and equations for deriving the angles of the halo: http://www.atoptics.co.uk/halo/22halfrm.htm

Sundogs:

Sundogs, also known as parhelia, are formed when light is refracted through hexagonal ice crystals in the atmosphere, similar to the formation of halos. However, in this case, the crystals are oriented horizontally, producing two bright spots on either side of the sun. To derive the angles at which sundogs occur, we can use similar equations and principles as for the halos. This website provides a detailed explanation and equations for deriving the angles of sundogs: http://www.atoptics.co.uk/halo/parhelia.htm

Coronas:

Coronas are formed when light is diffracted (scattered) by tiny water droplets in the atmosphere. The size of the water droplets and the wavelength of light determine the size and colors of the corona. To derive the size and colors of the corona, we can use the equations for diffraction and the properties of water droplets. This website provides a detailed explanation and equations for deriving the size and colors of coronas: http://www.atoptics