Mirror differences.

Paraboloid/spherical what are the differences (aside from contour?) which one would make the better scope?

OK I'll have a go at this one--we're talking about the reflective properties of conic sections. For a parabola, all incoming rays parallel to the axis are reflected to a single point, called the focus. Parallel rays at an angle to the axis are not so tightly focused, with the aberration increasing as the angle increases (coma). But with a sphere, even the rays parallel to the axis fail to focus on a single point, and the smear enlarges as the distance from the incoming ray and the axis increases (spherical aberration). (However, for a small portion of a sphere the reflected on-axis rays cluster near the point on the axis 1/2 of the distance between the center of the sphere and the sphere itself.) Thus a sphere is able to provide a decent image only if a very small portion of the sphere, relative to its radius, is used (high f/ ratio). Consequently, a 4" f/10 spherical mirror can be ok (and many inexpensive scopes are built that way), but at any shorter f/ ratio it is imperative that the mirror be parabolic.
George

p.s. For an ellipse, all rays emitted from one focus get reflected to the other focus (whispering galleries, ultrasonic kidney stone smashers). The circle is a special case of the ellipse: all rays emitted from its center get reflected to the center. For an hyperbola, all rays headed toward one focus from "outside" one branch get reflected to the other focus (the secondary of a classical cassegrain). Sorry, I'm a math teacher...

Phew, that's quite a lump for this old GI to digest. The reason I asked is that I purchased a Jaegers F7.4 spherical non-aluminized mirror. It was suggested on another forum that refigure it to paraboloid without a real explanation as to why. he did suggest a book, Standard Handbook for Telescope Making by Neale Howard, which I'm thinking of getting.

Never having ground a mirror let alone put a particular contour on one, the task seems rather daunting.