The focal length of the objective lens of a telescope is 50 cm. If the magnification of the telescope is 25, then the focal length of the eye-piece is

The magnification (M) of a refracting telescope is defined as the ratio of the focal length of the objective lens (fo) to the focal length of the eyepiece (fe). This relationship is expressed by the formula M = fo / fe. In this problem, the focal length of the objective lens (fo) is given as 50 cm and the magnification (M) is 25. By rearranging the formula to solve for the eyepiece focal length, we get fe = fo / M. Substituting the given values, fe = 50 cm / 25, which results in an eyepiece focal length of 2 cm. This calculation is a standard application of geometrical optics used to determine telescope parameters [1]. Therefore, the correct focal length for the eyepiece is 2 cm.

Sources

1. [1] https://spacemath.gsfc.nasa.gov/weekly/10Page32.pdf