# Light Ray Reflection from concave mirror

Suppose a ray of light hits a concave mirror and is parallel to principle axis but far away from it such that it doesn't follow paraxial ray approximation. Will it pass through focus or between focus and radius of curvature or between pole and focus?

Here pole, focus and radius of curvature mean the same thing as in paraxial ray approximation .

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It is depending upon the distance of ray from axis of mirror. –  Mr.ØØ7 Apr 27 '13 at 16:28
Removed the ridiculous down-vote by adding a +1. –  Antillar Maximus May 15 '13 at 11:31

Assuming mirror to be spherical section. C is the center of sphere.

See, Using trigonometry. $$x=d \times \sin(2\theta)$$ $$x=R\times\sin\theta$$

Eliminate $\theta$ and get $d$ : distance from Center of curvature as a function of $x$.

Verify for small theta where $\sin\theta\approx\theta$

If you just want to see that which side ray bents then see. $$d=\dfrac{R\times \sec\theta}2$$ which shows that $d\ge R/2$ . So, ray bends towards the pole as looses it paraxial character.

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Sorry for the rough image made in Paint . :P –  Mr.ØØ7 Apr 27 '13 at 16:40
The question of a general concave mirror can be answered depending on the deviation of curvature $\frac{1}{R}$. If deviation is positive, then the rays are closer on optical axis.