A divergent lens has a focal length of 20 cm. At what distance should an object of height 4 cm from the optical centre of the lens be placed so that its image is formed 10 cm away from the lens. Find the size of the image also. Draw a ray diagram to show the formation of image in above situation.

A divergent lens has a focal length of 20 cm. At what distance should

1.	A divergent lens has a focal length of 20 cm. At what distance should an object of height 4 cm from the optical centre of the lens be placed so that its image is formed 10 cm away from the lens. Find the size of the image also. Draw a ray diagram to show the formation of image in above situation.
Answer» Solution :Here focal length of given divergent (concave) LENS f = - 20 CM, height of the object h = + 4 cm and distance of image from the lens V = 10 cm. As the image formed by a concave lens is always virtual and ERECT, hence as per sign convention v = - 10 cm. As per lens formula `(1)/(v) - (1)/(u) = (1)/(f)`, we have `(1)/(u) = (1)/(v) - (1)/(f)` `therefore""(1)/(u) = (1)/((-10)) - (1)/((-20)) = - (1)/(10) + (1)/(20) = - (1)/(20)` `rArr` u = - 20 cm Thus, the object is placed at a distance 20 cm from the lens. Moreover `m = (h.)/(h) = (v)/(u)` `therefore` Size of image `h. = (v)/(u) xx h = ((-10))/((-20)) xx (+4) = + 2` cm A ray diagram to show the formation of image is given here in figure.