Question:
I just wanted to clarify whether there is any relationship
between the size of the primary mirror to the secondary. Obviously
there should be one, could someone tell me what it is? Lets consider
an example of an 8" and 10" primary mirror, what should be the size of
their secondary?
Answer:
Size of secondary depends on many factors.
1. Design of the telescope: Newtonian, Cassegrain etc. Here I will assume Newtonian.
2. The size of secondary also depends on the aperture and focal length.
3. Another factor to consider is the "fully illuminated field of view you desire". Example: If you are using a camera with the telescope, the fully illuninated field should be at least the size of the sensor.
The formula for the "Minor Axis" of an elliptical mirror
Lets take an example.
Consider 200mm mirror with 1000mm focal length.
Consider the distance between secondary mirror and focal plane to be 200mm.
Consider Canon 500D to be the imaging camera.
Fully illuminated field should be the diagonal of the imaging sensor = sqrt(22.2mm^2+14.8mm^2) = 27mm
a = (200 - 27)*200/1000 + 27 = 62mm.
Additional points:
The size of diagonal depends on ...
1. ... the primary's diameter - the larger the primary diameter, the larger the diagonal,
2. ... the primary's focal ratio - smaller the focal ratio, larger the diagonal,
3. ... size of tube and height of the focuser, the larger the radius of tube + height of focuser, larger the diagonal
4. ... the diameter of the field lens of the eyepiece, larger the field lens larger the diagonal required
the above condition can also be applied to cameras - larger the size of camera's sensor, larger the diagonal if you need to fully illuminate the entire sensor.
5. ... how large do you want your fully illuminated field to be, larger the fully illuminated view, larger the diagonal. Usually the value is take to be of the size of a full moon, i.e. half a degree. This condition no 5 is in practice, intermixed with the previous condition no 4.
Conversly:
The larger the diagonal size ...
... more the diffraction
... more light loss
... brighter the image at the eyepiece
Some related experience:
Telescope manufacturers in India put in puny diagonals in their telescopes, if you buy a 6inch telescope with a smaller diagonal, you are essentially getting light gathering of a 5 or a 4 inch telescope. The focuser needs to be of lesser height for an ideal diagonal and fully illuminated field. But for photography, the focuser needs to be of greater height so that camera can reach focus.
All this is written keeping a Newtonian telescope in mind.
You may see this article for more information:
http://www.garyseronik.com/?q=node/8