Paraxial rays and marginal rays question
A lens with spherical surfaces (i.e. surfaces that are a segment of a sphere) does not focus all parallel light rays onto a single point. Instead there is a focal surface called a caustic. This causes spherical aberation.
As long as the lens curvature is small, i.e. the ray is near to the optical axis (paraxial rays), the aberation is small and we approximate the caustic by a single point. However far from the axis the aberation is significant and the rays come to a focus at a different point.
As far as I know there is no simply way to show this. You'd need to sit down and calculate the path for the light ray as a function of distance from the optical axis, which isn't that difficult but is tedious.
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newera almost 3 years
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..
Brandon Enright over 10 yearsI texified your equations however the last one is obviously wrong since $\cos(0) = 1$.