question_answer

We wish to make a microscope with the help of two positive lenses both with a focal length of 20 mm each and the object is positioned 25 mm from the objective lens. How far apart the lenses should be so that the final image is formed at infinity?   JEE Main Online Paper (Held On 12 May 2012)

A) 20mm                                  

B)                        100mm

C)                        120mm    

D)                        80mm

Correct Answer: C

Solution :

                To obtain final image at infinity, object which is the image formed by objective should be at focal distance of eye-piece. By lens formula (for objective) \[\frac{1}{{{v}_{0}}}-\frac{1}{{{u}_{0}}}=\frac{1}{{{f}_{0}}}\]or\[\frac{1}{{{v}_{0}}}-\frac{1}{-25}=\frac{1}{20}\] \[\Rightarrow \]\[\frac{1}{{{v}_{0}}}=\frac{1}{20}-\frac{1}{25}=\frac{5-4}{100}=\frac{1}{100}mm\] \[\therefore \]\[{{v}_{0}}=100mm\] Therefore the distance between the lenses \[{{v}_{0}}=+{{f}_{e}}=100\,mm+20mm=120mm\]