Question

A converging lens of focal length $20\text{cm}$ and a diverging mirror of focal length $10\text{cm}$ are placed $5\text{cm}$ apart with their principal axes coinciding. Where should an object be placed so that its image falls on itself?

• A. $-50\text{cm}$
• B. $100\text{cm}$
• C. $50\text{cm}$
• D. $-100\text{cm}$

Answer 1

The correct option is B $100\text{cm}$

Let the object be placed at a distance $x$ from the pole of lens further away from the mirror.


From the figure,

$u=-x,f_1=20\text{cm}$

Using lens formula,

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

Substituting the data we get,

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

$\Rightarrow v=\frac{20x}{x-20}.....\left(1\right)$

For the ray to retrace its path, it should be incident normally on the convex mirror, or in other wrods the rays should pass through the center of curvature of mirror.

$\therefore v=+5+2\times 10=+25\text{cm}$

Substituting this in $\left(1\right)$ we get,

$+25=\frac{20x}{x-20}$

$25x-500=20x$

$\Rightarrow x=100\text{cm}$

Hence , option (b) is the correct answer.