Question

Prove that if an object is at a distance of twice the focal length from a lens the image is the same size as the object. Show this using an algebraic method

Answer 1

Here ,

let the focal length is f

object distance = 2 * focal length

object distance , do = 2 * f

Using the lens formula

1/f = 1/di + 1/do

1/f = 1/2f + 1/di

di = 2f

now , magnfication = -di/do

magnfication = -2f/2f

magnfication = -1

as magnfication is -1

hence , the object height is same as the image height