140330 From the Workshop #4...TimC

From the Workshop...#4
Tim Crawford
     In the last essay, I discussed the focal length and how it is up to you to choose which focal length is right for you.  I touched upon the relation between f/ratio, focal length and diameter of the scope’s objective. I realize most know the idea of focal length but I am using it as a springboard to less obvious conditions within the optical system.  One is that the shorter the focal length, the deeper the curve of the scope’s mirror.  This depth of the curve of your main objective mirror is called the sagitta.  This depth can be found by using a simplified equation:
s =(r*r)/2R.
     Here, r is the radius of the mirror and R is the mirror’s radius of curvature.  The radius of curvature is twice the focal length.  Imagine this:  you are holding a lit candle and standing in the center of a glass sphere whose inside surface is a mirror.  If wherever you look at the image of the reflection of the candle it is in focus, you are standing at the radius of curvature of the sphere.  Now, imagine that any part of this sphere is your mirror.  If you place a straight edge over the mirror, you can readily see the curve of your mirror's surface.  Already armed with your equation, you can determine the depth of this curve if you know its focal length.  Not only can you find this depth at the sphere's center but also at any of the points of the mirror's surface from the center to the edge of the mirror. These points are at different radii.  Therefore, it can be said there are an infinite number of "nested spheres" within your mirror's surface.  This will become important when we test our mirror. You will discover this in future essays of From the Workshop.
     In my next essay, I will clarify what takes place when you go to the eyepiece and see images in a typical reflecting telescope.