When an object is moved along the principal axis of a thin l

When an object is moved along the principal axis of a thin lens, the height of the image is five times the height of the object if the object is at point A (to the left of the lens) and also if the object is at point B, 20.0 cm farther from the lens, (a) Is the lens converging or diverging? (b) What is the focal length of the lens?

Solution

The magnification of a diverging lens is always less than 1 and hence, the image height is always less than the object height. However, in this question, it has been given that the image is 5 times larger than the object and so the lens must be a converging lens.

M=hi/ho = - di/do

Since hi/ho=5 (given) it implies that di=-5*do=-5*20=-100 cm

Also, 1/f = 1/do + 1/di

gives 1/f= 1/20-1/100=0.04

and so f=25 cm