i have no idea where to start:(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Optics derivations

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