The focal length of the objective and eyepiece of a microscope are . . .

Questions : The focal length of the objective and eyepiece of a microscope are 1.25 cm and 5 cm respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment. 

Doubt by Riddhi

Solution : 

Here normal adjustment refers to a configuration where the final image is formed at infinity.

f_o=1.25 cm
f_e=5 cm

m=30

When the final image is formed at infinity

m=-v_o/u_o(D/fe)
30=-v_o/u_o(25/5)
30=-v_o/u_o(5)
30/5=-v_o/u_o
6=-v_o/u_o
v_o=-6u_o

Using Thin Lens Formula

1/f_o=1/v_o-1/u_o
1/1.25=1/[-6u_o]-1/u_o
100/125=1/u_o[-1/6-1]
4/5=1/u_o[-7/6]
u_o=-35/24
u_o=-1.458
u_o≈-1.46 cm 

Hence, the object is at a distance of 1.46 cm away (left side) from the objective lens.