In the normal adjustment of an astronomical telescope, the objective and eyepiece are 36 cm apart. If the magnifying power of the telescope is 8, find the focal lengths of the objective and eyepiece.

Step-by-step solution

In the normal adjustment of an astronomical telescope, the distance between the objective and the eyepiece is given by L = f_o + f_e . Given L = 36 cm , we have f_o + f_e = 36 . The magnifying power M of an astronomical telescope in normal adjustment is given by M = f_o f_e . Given M = 8 , we have f_o f_e = 8 , which implies f_o = 8f_e . Substituting f_o = 8f_e into the first equation: 8f_e + f_e = 36 . 9f_e = 36 f_e = 4 cm . Then f_o = 8 4 = 32 cm . Answer: F _ o =32 ~cm , F _ e =4 ~cm