Which distance is equal to the focal length of a lens?
(A) the distance between a distant object and the image
(B) the distance between the image of a close object and the centre of the lens
(C) the distance between the image of a distant object and the centre of the lens
(D) the distance between two principal foci
Solutions: Option C
Focal length f is the distance between the focal point and the centre of the lens (optical centre).
Note that only when parallel rays of light enter a converging lens, the rays will converge to a point. That point is considered to be focal point F (principal focus). The distance between focal point F and the optical centre is the focal length f. Refer to below.
As none of the options is similar to the above definition, you have to consider that the rays from a distant (far away) object are considered parallel. Hence the sharp image formed on the screen is considered the forcal point F of the lens and the distance between the image and the optical centre is the focal length f.
If it is a close object, the rays entering are not considered parallel. Hence even if the rays converged to a point, that point is NOT focal point F and the distance between this converged point and the optical centre is NOT focal length f.