question_answer

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be:                                     [JEE Main 8-4-2019 Morning]

A) 40 cm from the convergent mirror, same size as the object

B) 20 cm from the convergent mirror, same size as the object

C) 20 cm from the convergent mirror, twice the size of the object

D) 40 cm from the convergent lens, twice the size of the object

Correct Answer: B

Solution :

Note : There will be 3 phenomenon (i) Refraction from lens (ii) Reflection from mirror (iii) Refraction from lens After these phenomena. Image will be on object and will have same size. None of the option depicts so this question is Bonus 1st refraction \[u=40cm;f=+20cm\] \[\Rightarrow \]\[\text{v}=+40cm\,(image\,{{I}_{1}})\] and\[{{m}_{1}}=-1\]for  reflection \[u=-20cm;f=-10cm\] \[\Rightarrow \text{v}=-20cm\,(image\,{{I}_{2}})\] and \[{{m}_{2}}=-1\] 2nd refraction \[u=40cm;\text{ }f=+20cm\] \[\text{v}=+40cm\left( \text{image }{{I}_{3}} \right)\] and \[{{m}_{3}}=-1\] Total magnification\[={{m}_{1}}\times {{m}_{2}}\times {{m}_{3}}=1\]and final image is formed at distance 40cm from convergent lens and is of same size as the object