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 \[v=O{{C}_{1}}=x+10\] \[\Rightarrow \] \[x=v-10=60-10=50\,\,cm\]