Focal length of the objective lense (f_0bj) = 1.25 cm

Focal length of the eyepiece (f_eye) = 5 cm

Distance of vision (d) = 25 cm

Angular magnification of the compound microscope = 30X

Total magnification power of the compound microscope (m)= 30

Angular magnification of the eyepiece

m_eye = (1+d/f_eye) = (1+25/5) = 6

Angular magnification of the object (m_obj) is related to m_eye

Thus, m_obj = m/ m_eye = 30/6 = 5

Also, m_obj = image distance for the objective lens (v_obj)/ Objective distance for the objective lens (-u_obj)

5 = v_obj /-u_obj

v_obj  = -u_obj x 5                                      (i)

Using lens formula

1/ v_obj  - 1/ u_obj = 1/f_obj

1/1.25= 1/-5 u_obj - 1/ u_obj

1/1.25= -6/ u_obj

u_obj = -6/5 x 1.25 = -1.5 cm

v_obj = -5 u_obj = -5 x (-1.5) = 7.5 cm

The object should be placed 1.5 cm away from the objective lens.

Using lens formula

1/ v_eye  - 1/ u_eye = 1/f_eye

Where,  v_eye  = image distance for the eyepiece = -d = -25 cm

u_eye = Object distance for the eyepiece

1/ u_eye = 1/ v_eye  -  1/f_eye = -1/25 - 1/5 = -6/25

u_eye = 4.17 cm

Separation between the objective lens and eyepiece = u_eye + v_obj = 4.17 + 7.5 = 11.67 cm