Question

Setting up a movie in the park, the projector (object) is placed 50.0 m from the screen. A lens of focal length +15.0 m is set a distance of 20.0 m from the projector. A second lens of focal length +30.0 m must be set at what location so that the image is focused on the screen?

Answer 1

first cae image will be form at v

so. 1/v -1/u = 1/f

or, 1/v = 1/f + 1/u = 1/15+ 1/-20 = 1/15 - 1/20 [as u= -20cm ]

so, v = +60 cm   

so first image will not focus on screen as it is 50 cm away from projector.

now let the position of second lens be x from first lens

so, 1/v - 1/u = 1/f

or, 1/(30-x) - 1/(60-x) =1/f = 1/30

solve 30/(1800-x^2 -90x) = 1/30

or, x^2 +90x -1800 = -900

or,  x^2 +90x -900 =0

or, x= 9 cm

so, it might be place at 20+9 = 29 cm from prohrctor or 9 sm fromsecond lens