The magnification of a compound microscope is 20. The focal length of the eyepiece is 5 cm and the image is formed at near point (25 cm). The magnification of the objective lens is 

Compound microscope: 

• It is used for much larger magnifications.
• Two lenses are used with one lens compounding the effect of the other.

where fo is the focal length of the objective lens,  fe  is the focal length of the eyepiece, h is the object height, h' is the size of the first image

• A compound microscope uses two lenses i.e., objective lens and eyepiece. 
  • Objective lens: lens nearest to the object forming a real, inverted, and magnified image of the object.
  • Eyepiece: produces a final image that is enlarged and virtual.

​CALCULATION:

Given: magnification of compound microscope(m) = 20, focal length of eye piece (f_e) = 5 cm and image is formed at near point (v= D) = 25 cm.

• Linear magnification due to eyepiece:

\(⇒ m_{e} = 1+\frac{D}{f} = 1+ (\frac {25}{5} )= 6\)

• Total magnification is given by:

⇒ m = m_o × m_e,

where m_o is the magnification due to the objective lens.

• Magnification due to the objective lens is given by:

\(⇒ m_{o} = \frac {m}{m_{e}} = \frac {20}{6} = 3.33\)

• Hence option 3) is correct.