In this question why is it that we use focal length of eyepiece in (a) part

Dear Student,
We use the focal length of eyepiece to determine the distance of image v1 formed from the objective,And from that we determine actual distance of object u1 as shown in the solution.
Focal length of the objective lens, f₁ = 2.0 cm

Focal length of the eyepiece, f₂ = 6.25 cm

Distance between the objective lens and the eyepiece, d = 15 cm

(a) Least distance of distinct vision,

∴Image distance for the eyepiece, v₂ = −25 cm

Object distance for the eyepiece = u₂

According to the lens formula, we have the relation:

Image distance for the objective lens,

Object distance for the objective lens = u₁

According to the lens formula, we have the relation:

Magnitude of the object distance, = 2.5 cm

The magnifying power of a compound microscope is given by the relation:

Hence, the magnifying power of the microscope is 20.

(b) The final image is formed at infinity.

∴Image distance for the eyepiece,

Object distance for the eyepiece = u₂

According to the lens formula, we have the relation:

Image distance for the objective lens,

Object distance for the objective lens = u₁

According to the lens formula, we have the relation:

Magnitude of the object distance, = 2.59 cm

The magnifying power of a compound microscope is given by the relation:

Hence, the magnifying power of the microscope is 13.51.
Hope it helps you!!!
Regards