In an astronomical telescope, the magnifying power
(M) is given by the ratio of the focal length of the objective
(fo) to the focal length of the eyepiece
(fe) :
M=‌ Given that the magnifying power is 7 , we have:
7=‌This implies:
fo=7fe Also, it is given that the objective and eyepiece are 32 cm apart. The separation between the objective and the eyepiece in a telescope adjusted for normal vision is equal to the sum of their focal lengths:
fo+fe=32‌cmSubstituting the value of
fo from the first equation
fo=7fe into the second equation, we get:
7fe+fe=32Combining like terms:
8fe=32Solving for
fe, we get:
fe=‌=4‌cmNow, substituting this back to find
fo :
fo=7×4=28‌cm Therefore, the focal lengths of the objective and the eyepiece are:
‌fo=28‌cm‌fe=4‌cmHence, the correct option is:
Option D:
fo=28‌cm and
fe=4‌cm