Question

For a particular converging lens, an object a certain distance to the left of the lens produces a clear image on a a screen a distance 30.2 cm to the right of the lens. When a second lens is placed 15.4 cm to the right of the first lens, the screen has to be moved 18.7 cm to the right of its previous location to produce a clear image.

Determine the focal length of the second lens.

Answer 1

Distance of the image from the first lens i = 30.2 cm

Distance of the second lens from first lens d = 15.4 cm

Virtual obeject distance from second lens u = 30.2cm - 15.4 cm

                                                                 = 14.8 cm

Final image distance from second lens v = u + 18.7 cm

                                                           = 14.8 cm + 18.7 cm

                                                           = 33.5 cm

Let the focal length of the second lens be f .

From the relation ( 1/ v) - (1/ u) = ( 1/ f)

                         ( 1/ 33.5) -(1/14.8) = ( 1/ f)

                                f = (14.8 x 33.5) / (14.8 - 33.5)

                                  = -26.51 cm