In the normal adjustment of an astronomical telescope, the objective and eyepiece are 32 ~cm apart. If the magnifying power of the telescope is 7, 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 = 32 cm , we have f_o + f_e = 32 . The magnifying power M of an astronomical telescope in normal adjustment is given by M = f_o f_e . Given M = 7 , we have f_o f_e = 7 , which implies f_o = 7f_e . Substituting f_o = 7f_e into the first equation: 7f_e + f_e = 32 . 8f_e = 32 f_e = 4 cm . Using f_o = 7f_e , we get f_o = 7 4 = 28 cm . Therefore, f_o = 28 cm and f_e = 4 cm . Answ