A convex lens forms inverted image of a real object on a fixed screen. The size of image is 9 cm . When lens is displaced 40 cm along principle axis it again forms a real image of size 4 cm on the screen. Focal length of the lens is .

Step-by-step solution

Since           m 1   m 2 = 1       ⇒       h 1 h 0   h 2 h 0 = 1 h 0 =   h 1   h 2 = 6 c m for first position of the lens m = - 3 2 = -   x   +   40 x ⇒       3 x = 2 x + 80 ⇒       x =   80 u = - x , y = ( 40 + x ) 1 f = 1 120 - 1 - 80 ⇒ f = 48   cm