# Paraxial rays and marginal rays question

Paraxial rays are found to focus far away the lens whereas marginal rays focus near to the lens, why? I didn't find satisfactory answer in my academic book..

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The formula for the focus of marginal rays is given by $R - \frac{R}{\cos{\theta}}$ where $\theta$ is the angle made by the marginal ray with the line joining it's point of incidence with centre of curvature. We can see that for marginal rays $\theta$ is large hence the focus is small. Thus marginal rays converge close to the lens (for concave lenses) and diverge from a nearer point (for convex lenses). In fact, for paraxial rays $\theta$ is approximately $0$ and so $F = R -\frac{R}{\cos(0)} = R/2$
I texified your equations however the last one is obviously wrong since $\cos(0) = 1$. –  Brandon Enright May 29 '13 at 6:27