A needle placed at $30\ cm$ from the lens forms an image on a screen placed $60\ cm$ on the other side of the lens. Determine the focal length.

Given,

The needle is placed at $30\ cm$ from the lens, it forms an image on a screen placed at $60\ cm$ on the other side of the lens.

Object distance, $u=-30cm$

Image distance, $v=60cm$

Focal length, $f$

Applying lens formula,

$\dfrac 1f=\dfrac 1v-\dfrac 1u\\\implies \dfrac 1f=\dfrac 1{60}-\dfrac 1{-30}\\\implies \dfrac 1f=\dfrac {1+2}{60}\\\implies f=20cm$

Since the image is formed on the other side of the lens, the image is real. also, the focal length is positive. So, it is a convex lens.