question_answer

A luminous object is placed at a distance of \[30\,\,cm\] from the convex lens of focal length\[20\,\,cm\]. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature \[10\,\,cm\] be placed in order to have an upright image of the object coincident with it?

A) \[60\,\,cm\]                      

B) \[50\,\,cm\]

C)  \[30\,\,cm\]                     

D)  \[20\,\,cm\]

Correct Answer: B

Solution :

The given situation can be shown as Here,     \[u=OC=-30\,\,cm\]                 \[f=20\,\,cm\] By using,\[\frac{1}{v}=\frac{1}{f}+\frac{1}{u}\]                 \[=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}\] \[\Rightarrow \]               \[v=60\,\,cm\] To obtain upright image of \[O\] at \[O\] itself                 \[v=O{{C}_{1}}=x+10\] \[\Rightarrow \]               \[x=v-10=60-10=50\,\,cm\]