Variation of image vergence with change in object distance for telescopes: the general case

Three formulas are given and derived which can be used to evaluate the relationship between image vergence and object position for any two-lens system and will be very useful in the special case of telescopes. A corresponding formula for afocal telescopes has been published previously. The formulas presented here are applicable to all non-afocal (focal) telescopes, including particular types such as near point telescopes. All that is required for their evaluation is the positions of one pair of conjugate planes, the corresponding magnification, and the lens separation. The formulas can be used to estimate such quantities as a working or useful depth of field and accommodation demand, particularly when the optical system is not used at its design conjugates. A numerical example is presented.