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?   [AIPMT 1998]

A)  12 cm

B)                  30 cm

C) 50 cm

D)                   60 cm

Correct Answer: C

Solution :

The lens formula is \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]

we have

\[u=-30\,cm,\,\,f=20\,cm\]

\[\therefore \]    \[\frac{1}{20}=\frac{1}{v}-\frac{1}{-30}\]

or         \[\frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{3-2}{60}=\frac{1}{60}\]

\[\therefore \]    \[v=60\,cm\]

The ray diagram for the problem is shown as follows:

For the image (I) coincident with object (O) the rays after refraction from the lens must fail on the convex mirror normally or the rays refracted from lens must meet at C.

\[\therefore \]      \[LC=v=60\text{ }cm\]

Thus, distance between lens and mirror

\[LM=60-10=50\text{ }cm\]