Question

A point luminous object is placed at a distance of $30\text{cm}$ from the convex lens of focal length $20\text{cm}$ on the other side of the lens. At what distance from the lens, a convex mirror of radius of curvature $10\text{cm}$ 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 $50\text{cm}$


For refraction through convex lens:

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

Using lens formula,

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

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

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

For reflection from convex mirror:

Image is formed by convex lens at $60\text{cm}$ on right side.

In order to obtain an image at the object's position, the rays should incident perpendicularly on the convex mirror, that is, they must seem to pass through the centre of curvature of the convex mirror.

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