A concave lens of focal length f forms an image which is n times the size of the object. What is the distance of the object from the lens in terms of f and n ?

Q:  A concave lens of focal length f forms an image which is n times the size of the object. What is the distance of the object from the lens in terms of f and n ?

Sol: The concave lens formula is

$\large \frac{1}{v} – \frac{1}{u} = \frac{1}{f} $

Multiplying by u ,

$\large \frac{u}{v} – 1 = \frac{u}{f} $

$\large \frac{1}{n} – 1 = \frac{u}{f} $

$\large u = (\frac{1 – n}{n} ) f $