I examined the use of a single lens system for the available range of focal lengths, for the required magnification and found that a focal length of at most 100 mm would be required to sufficiently cover the object distance range. This would greatly compromise with the f-number and hence lead to a lot more spherical aberrations.
Therefore, a two lens system would be more useful to implement. Using an eyepiece of 1” puts an additional constraint on the system such that the separation between the lenses must now at least equal or be greater than half the image distance from the first lens to ensure that no light from the light cone is lost. This is clarified in the schematic. The image from the first lens in absence of the second lens would form at point A, subtending an angle θ. In order to ensure that no part this light cone emerging from the first lens is lost, the second lens must be placed at a distance atleast v/2 from the first lens.
A combination of 125mm focal length 2” diameter objective with a 250 mm 1” eyepiece covers the required range of object distances (650mm to 1500 mm). Increasing the focal length of the eye piece increases the minimum object distance accessible to 700 mm.
A glance at the accessible u, v points shows that all magnifications are not possible at a given object distance. To image the entire surface of the test mass, a distance of at least 1.25m is required from the objective, while a beam spot of 1'' diameter can be imaged easily at upto 1200 mm from the objective . This holds true even for the 150-250 mm biconvex 2" lens combination proposed earlier.
If this sounds reasonable, we could proceed with ordering the lenses.