Question

A telescope has an objective lens with a focal length of 50 cm. An astronomer wants his telescope to have a magnification of (minus) 20. What should be the focal length of his eyepiece?

Can you please draw relevant diagrams and explain the working out?

The answer should be 2.5cm.

Answer 1

The magnification of a telescope is given by the formula :-

m = -f_o/f_e(1+f_e/D)

Where, the above formula is used when the telescope forms the image at the normal distance of vision. Here, D = 25 cm.

Second arrangement of the telescope has the image formation at infinity, where D = infinity.

m = -f_o/f_e

where, f_o = focal length of the objective

f_e = focal length of the eye-piece

The magnifying power of the telescope is equal to the ratio of the angle formed by final images at eye to the angle subtended by object at eye.