Question

A convex lens of focal length $15$cm is placed in front of a plane mirror at a distance $25$cm from the mirror. Where on the optical axis and from the centre of the lens should be small object be placed such that the final image coincides with the object?

• A. $15$cm and on the opposite side of the mirror
• B. $15$cm and between the mirror and the lens
• C. $7.5$ cm and on the opposite side of the mirror
• D. $7.5$cm and between the mirror and the lens

Answer 1

The correct option is A $15$cm and on the opposite side of the mirror

Let the object be placed at a distance $o$ as shown in the figure.

Using the Lens maker equation, $\frac{1}{o}+\frac{1}{i}=\frac{1}{f}$

As convex lens is a converging lens, $f=+15\text{cm}$

$\therefore i=\frac{of}{o-f}$

This is reflected by the plane mirror to get the image which acts as an object for the lens.

And the distance between lens and mirror is $25\text{cm}$

This means, $i-25=o_2+25$ (Image-Object coincidence condition)

i.e., $i-50=o_2$

Applying lens maker formula on the new object,

$i_2=\frac{o_{2}f}{o_2-f}$

For the image to coincide at the object, $i_2=o$

$\Rightarrow (o_2-f)\left(o\right)=o_{2}f\Rightarrow (i-50-15)\left(o\right)=(i-50)\left(15\right)$

Solving, the quadratic, we get $o=15$