Question

A converging lens (f = 13.0 cm) is located 40.6 cm to the left of a diverging lens (f = -7.18 cm). A postage stamp is placed 49.0 cm to the left of the converging lens. (a) Locate the final image of the stamp relative to the diverging lens. (b) Find the overall magnification.

Answer 1

here,

for the converging lens

the focal length , f1 = 13 cm

the object distance , do1 = - 49 cm

let the image distance be di1

using the lens formula

1/f1 = 1/di1 - 1/do1

1/13 = 1/di1 - 1/(-49)

di1 = 17.7 cm

for the diverging lens

the focal length , f2 = - 7.18 cm

the object distance , do2 = - (40.6 - di1 ) = - 22.9 cm

let the image distance be di2

using the lens formula

1/f2 = 1/di2 - 1/do2

1/(-7.18) = 1/di1 - 1/(-22.9)

di2 = - 5.47 cm

the final image is 5.47 cm to the left of diverging lens

b)

the overall magnification , m = (di1 /do1) * ( di2 /do2)

m = (17.7)/(-49) * ( (-5.47))/(- 22.9)

m = - 0.086