An object of height 4 cm is placed in front of a concave lens of focal length 40 cm. If the object distance is 60 cm, find the position and height of the image.

Explanation

` (i) 1/f = 1/v -1/u " " therefore 1/u = 1/f + 1/u`
` therefore 1/u = 1/( - 40 cm) + 1/( - 60 cm) = - (1/( 40 cm) + 1/( 60 cm) )`
` = - ((3+2)/(120 cm) ) = - 5/120 cm `
` v - (120 cm)/5 = - 24 cm `
The image is formed at 24 cm from the lens. It is on the same side as the object.
(ii) ` h_(2)/h_(1) = u/v " " therefore h_(2) = v/u h_(1)`
` therefore h_(2) = ((-24 cm)/(- 60 cm)) xx 4 cm = 0.4 xx 4 cm = 1.6 cm`
The height of the image is 1.6 cm