Question

An upright object is placed at a distance of $40cm$ in front of a convergent lens of focal length $20cm$. A convergent mirror of focal length $10cm$ is placed at a distance of $60cm$ on the other side of the lens. The position and size of the final image will be

• A. $40cm$ from the convergent lens, same size as the object
• B. $20cm$ from the convergent mirror, same size as the object
• C. $20cm$ from the convergent mirror, twice the size as the object
• D. $40cm$ from the convergent mirror, twice the size as the object

Answer 1

The correct option is A $40cm$ from the convergent lens, same size as the object


There will be $3$ phenomena
(i) Refraction from lens
(ii) Reflection from mirror
(iii) Refraction from lens

$1^{st}$ refraction from lens: $u=-40cm;f=+20cm$
$\Rightarrow v=+40cm\left(image{I}_1\right)$
and $m_1=-1$
Reflection from concave mirror:
$u=-20cm;f=-10cm$
$\Rightarrow v=-20cm\left(image{I}_2\right)$
and $m_2=-1$
$2^{nd}$ refraction from lens
$u=-40cm;f=+20cm$
$\Rightarrow v=+40cm\left(image{I}_3\right)$
and $m_3=-1$
Total magnification $=m_1\times m_2\times m_3=-1$
$\therefore$ Final image is formed at distance $40cm$ from the convergent lens and is of same size as the object.