COMEDK 2024 Shift 1 Paper

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=‌

fo

fe

Given that the magnifying power is 7 , we have:
7=‌

fo

fe

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=32‌cm
Substituting the value of fo from the first equation fo=7fe into the second equation, we get:
7fe+fe=32
Combining like terms:

8fe=32
Solving for fe, we get:
fe=‌

32

8

=4‌cm
Now, substituting this back to find fo :
fo=7×4=28‌cm

Therefore, the focal lengths of the objective and the eyepiece are:
‌fo=28‌cm
‌fe=4‌cm
Hence, the correct option is:
Option D: fo=28‌cm and fe=4‌cm