Question 202 of 295

A diverging lens with magnitude of focal length $25cm$ is placed at a distance of $15cm$ from a converging lens of magnitude of focal length $20cm$. A beam of parallel light falls on the diverging lens. The final image formed is:

AReal and at a distance of $6cm$ from the convergent lensBReal and at a distance of $40cm$ from convergent lensCVirtual and at a distance of $40cm$ from convergent lensDReal and at a distance of $40cm$ from the divergent lens

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Answer: (B) Real and at a distance of $40cm$ from convergent lens

Diverging lens forms the image at its focus. The image formed by diverging lens is the object for converging lens.

$∴$ Distance of the object from converging lens is $40cm$ i.e., object is at double focal point.

$∴$ Image forms at double focal point on the other side of the lens.
$\dfrac{1}{v}-\dfrac{1}{4}=\dfrac{1}{f}$
$\dfrac{1}{v}-\dfrac{1}{\left(-40\right)}=\dfrac{1}{20}$
$\dfrac{1}{v}+\dfrac{1}{40}=\dfrac{1}{20}$
$\dfrac{1}{v}=\dfrac{1}{20}-\dfrac{1}{40}=\dfrac{1}{40}$
$v=40$