Revision as of 02:14, 17 January 2014 edit Srleffler (talk \| contribs) Extended confirmed users, Pending changes reviewers, Rollbackers 45,977 edits Put formula in image caption into plain text, so size isn't so glaringly different. Simplify caption. The reader can see that it is a plot. ← Previous edit		Revision as of 02:23, 17 January 2014 edit undo Srleffler (talk \| contribs) Extended confirmed users, Pending changes reviewers, Rollbackers 45,977 edits The accuracy statement is confusing because it follows the second-order cosine expression immediately with a statement about the first-order approximation, without explanation. The whole approximation either passes or fails. Next edit →
Line 26: :<math> \cos \theta \approx 1 - { \theta^2 \over 2 } \ .</math> The ~~paraxial~~second-order approximation is accurate within 0.5% for angles under about ~~5° for the cosine approximation and~~ 10° ~~for the sine approximation~~, but its inaccuracy grows significantly for larger angles.<ref> {{cite web \| title=Paraxial approximation error plot \| url=http://www.wolframalpha.com/input/?i=Plot~~%5B%7B~~[{%28x+Deg+-+Sin~~%5Bx~~[x+Deg~~%5D~~]%29%2FSin~~%5Bx~~[x+Deg~~%5D~~]%2C+%28Tan~~%5Bx~~[x+Deg~~%5D~~]+-+x+Deg%29%2FTan~~%5Bx~~[x+Deg~~%5D~~]%2C+%281+-+Cos~~%5Bx~~[x+Deg~~%5D~~]%29%2FCos[x+Deg]%~~5Bx~~2C%281-%28x+Deg%5D29^2%7D2F2-cos[x+Deg]%29%2FCos[x+Deg]}%2C+~~%7Bx~~{x%2C+0%2C+15~~%7D%5D~~}] \| work=[[Wolfram Alpha]] \| publisher=[[Wolfram Research]]

Paraxial approximation: Difference between revisions