Let the focal length of an eye-piece be 2.5 cm. For a telescope of magnification 100, the focal length of the objective should be:

Concept:

• Magnification produced by a spherical mirror or lens gives the relative extent to which an object is magnified with respect to the object's size.
• Magnification is the ratio of the objective's focal length to the eyepiece's focal length.

Calculation:

Given data Focal length of eyepiece f_E = 2.5 cm

Magnification (M) = 100

f_O is focal length of objective.

∴ M = \(\frac{f_O}{f_E}\)

∴ 100 = \(\frac{f_O}{2.5}\)

∴ f_O = 250 cm