Optics Question 355
Question: The focal lengths of the objective and the eye-piece of a compound microscope are 2.0 cm and 3.0 cm respectively. The distance between the objective and the eye-piece is 15.0 cm. The final image formed by the eye-piece is at infinity. The two lenses are thin. The distances in cm of the object and the image produced by the objective measured from the objective lens are respectively
[IIT 1995]
Options:
A) 2.4 and 12.0
B) 2.4 and 15.0
C) 2.3 and 12.0
D) 2.3 and 3.0
Show Answer
Answer:
Correct Answer: A
Solution:
When final image is formed at infinity, length of the tube $ =v _{o}+f _{e} $
$ \Rightarrow 15=v _{o}+3 $
$ \Rightarrow v _{o}=12\ cm $ For objective lens $ \frac{1}{f _{o}}=\frac{1}{v _{o}}-\frac{1}{u _{o}} $
$ \Rightarrow \frac{1}{(+2)}=\frac{1}{(+12)}-\frac{1}{u _{o}} $
$ \Rightarrow u _{o}=-2.4cm $
