Question

If an object is placed at a distance of 12 cm from a convex lens of focal length 16 cm then calculate the image distance from the lens?

Answer 1

Given :

• Object distance (u) = 12 cm
• Focal length (f) = 16 cm

To Find :

• Image distance from the lens (v)

Solution :

The object distance is negative.

•°• u = - 12 cm.

Since, it is a convex lens, the focal length will be positive.

Lens formula :

$\large{\boxed{\sf{\red{\dfrac{1}{f}\:=\:\dfrac{1}{v}-\dfrac{1}{u}}}}}$

Block in the data,

$\sf{\dfrac{1}{16}\:=\:\dfrac{1}{v}-\dfrac{1}{-12}}$

$\mathtt{\dfrac{1}{16}\:=\:\dfrac{-12-v}{-12v}}$

$\mathtt{-12v\:=\:16(-12-v)}$

$\mathtt{-12v\:=\:-192\:-\:16v}$

$\mathtt{-12v+16v=-192}$

$\mathtt{4v=-192}$

$\sf{v\:=\:{\cancel{\dfrac{-192}{4}}}}$

$\sf{v\:=\:-\:32}$

Image distance is negative, since the object distance is less than the focal length.

$\large{\boxed{\sf{\blue{Image\:distance\:=\:v\:=\:-\:32\:cm}}}}$