question_answer

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30cm is 2 cm.  If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image [IIT-JEE (Screening) 2003]

A)            1.25 cm                                   

B)            2.5 cm

C)            1.05 cm                                   

D)            2 cm

Correct Answer: B

Solution :

                   Convex lens will form image \[{{I}_{1}}\] at it?s focus which acts like a virtual object for concave lens. Hence for concave lens \[u=+4\,cm\], \[f=20\]\[cm\,.\] So by lens formula \[\frac{1}{-20}=\frac{1}{v}-\frac{1}{4}\Rightarrow v=5\,cm\] i.e. distance of final image \[({{I}_{2}})\] from concave lens \[v=5\,cm\] by using \[\frac{v}{u}=\frac{I}{O}\Rightarrow \frac{5}{4}=\frac{I}{2}\Rightarrow ({{I}_{2}})=2.5\,cm\]