Final answer:
The focal length of the eyepiece for the refracting telescope at the Lick Observatory in California would give a magnification of 1000x is 17.3748 mm.
Step-by-step explanation:
The magnification of a telescope is given by the ratio of the focal length of the objective lens to the focal length of the eyepiece. In this case, the objective lens has a focal length of 57 ft, which is equivalent to 17,374.8 mm. To find the focal length of the eyepiece that would give a magnification of 1000x, we can use the formula:
Magnification = Focal Length of Objective / Focal Length of Eyepiece
Rearranging the formula, we have:
Focal Length of Eyepiece = Focal Length of Objective / Magnification
Substituting the values, we get:
Focal Length of Eyepiece = 17,374.8 mm / 1000
Focal Length of Eyepiece = 17.3748 mm