aplantic points and it's uses
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Answer:
Having seen the basic laws that govern how lenses and mirrors work, now we will examine some ways in which one of the basic aberrations of lens and mirror systems, spherical aberration, can be eliminated in a mathematically exact fashion.
In the case of mirrors, it can be shown from geometry that a parabolic mirror reflects parallel rays of light towards its focus, an elliptical mirror reflects rays coming from one of its foci to the other focus, and a hyperbolic mirror reflects rays of light aimed at the focus behind the mirror to the focus in front of the mirror. These are the curves which eliminate spherical aberration when used with mirrors. However, they do not eliminate other limitations of optical systems, such as coma, as was noted when the Ritchey-Chrètien telescope design was discussed.
Of course, the Newtonian telescope design, for example, is still quite useful, even if it has some coma, and other aberrations. Every lens and every mirror results in the loss of some light, and so a Newtonian, particularly one with a long focal ratio, represents a very good compromise between the correction of aberrations on the one hand, and preserving as much as possible of the incoming starlight.
It is not nearly so obvious what the equation might be for the ideal shape of a lens that focuses parallel, on-axis rays to a single point, thus eliminating spherical aberration.
Explanation: