Question

A convex lens has a focal length of 16.5 cm. Where on the lens axis should an object be placed in order to get a virtual, enlarged image with a magnification of 1.90?

Answer 1

Object should be placed at a distance, u = 7.8 cm

Given:

focal length of convex lens, F = 16.5 cm

magnification, m = 1.90

Solution:

Magnification of lens, m = -
`(v)/(u)`

where

u = object distance

v = image distance

Now,

1.90 =
`(v)/(u)`

v = - 1.90u

To calculate the object distance, u by lens maker formula given by:

`(1)/(F) = (1)/(u)+ (1)/(v)`

`(1)/(16.5) = (1)/(u)+ (1)/(- 1.90u)`

`(1)/(16.5) = (1.90 - 1)/(1.90u)`

`(1)/(16.5) = ( 0.90)/(1.90u)`

u = 7.8 cm

Object should be placed at a distance of 7.8 cm on the axis of the lens to get virtual and enlarged image.