Content deleted Content added
Added link to ScienceWorld article |
Added link to live plot for errors in all three paraxial approximations |
||
Line 33:
:<math> \cos \theta \approx 1 - { \theta^2 \over 2 } \ .</math>
The paraxial approximation is accurate within 0.5% for angles under about 10° 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+Deg%5D%29%2FSin%5Bx+Deg%5D%2C+%28Tan%5Bx+Deg%5D+-+x+Deg%29%2FTan%5Bx+Deg%5D%2C+%281+-+Cos%5Bx+Deg%5D%29%2FCos%5Bx+Deg%5D%7D%2C+%7Bx%2C+0%2C+15%7D%5D
| work=[[Wolfram Alpha]]
| publisher=[[Wolfram Research]]
| accessdate=15 January 2014}}</ref>
<!-- This plots Plot[{(x Deg - Sin[x Deg])/Sin[x Deg], (Tan[x Deg] - x Deg)/Tan[x Deg], (1 - Cos[x Deg])/Cos[x Deg]}, {x, 0, 15}] -->
For larger angles it is often necessary to distinguish between [[meridional ray]]s, which lie in a plane containing the [[optical axis]], and [[sagittal ray]]s, which do not.
| |||