Question

A luminous object is placed at a distance of $30\text{cm}$ from the convex lens of focal length $20\text{cm}$. At what distance from the lens, a convex mirror of radius of curvature $10\text{cm}$ should be placed in order to have an upright image of the object coincident with it ?

• A. $12\text{cm}$
• B. $30\text{cm}$
• C. $50\text{cm}$
• D. $60\text{cm}$

Answer 1

The correct option is C $50\text{cm}$


Refraction through convex lens

$u=-30\text{cm};f=+20\text{cm}$

Using lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}=\frac{1}{20}-\frac{1}{30}$

$\therefore v=+60\text{cm}$

Image formed by convex lens is at $60\text{c}m$ on its right and this image acts an object for the convex mirror.

Reflection at convex mirror:

In order to obtain the image formed by the convex mirror at the object's position, the object must be placed on its centre of curvature.

$\therefore d+R=60$

$\Rightarrow d=60-10=+50\text{cm}$

Hence, option $\left(c\right)$ is correct.
$$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: For spherical mirrors, if object is}\\ \text{placed on its centre of curvature, its}\\ \text{image coincide with the object itself.}\end{array}$$