An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification 6, gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to ______ cm.
Numerical value type. Enter your answer.
Answer: 25
As a simple microscope (image at the near point): $1 + \dfrac{D}{f_o} = 6 \Rightarrow f_o = 5$ cm.
Used as the objective of a compound microscope with tube length $L = 60$ cm and final image at infinity:
$$M = \frac{L}{f_o}\cdot\frac{D}{f_e} = \frac{60}{5}\cdot\frac{25}{f_e} = 12 \Rightarrow f_e = 25\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics