Question

An object and two lenses are arranged so that the object is to the left of and 40cm from a converging lens. The magnitude of the focal length of the first ens is 25cm. A diverging lens is 100cm to the right of the first lens and the magnitude of the focal length is 15cm. Find the location of the final image relative to the original object, the overall magnification.

Answer 1

here,

for the first lens

the object distance ,d01 = 40 cm

focal length , f1 = 25 cm

let the image distance be di1

using the lens formula

1/f1 = 1/di1 + 1/do1

1/25 = 1/di1 + 1/40

solving for di1

di1 = 66.7 cm

for the seccond lens

the object distance , do2 = 100 - di1 = 33.3 cm

the focal length , f2 = - 15 cm

let the image distance be di2

using the lens formula

1/f2 = 1/di2 + 1/do2

- 1/15 = 1/di2 + 1/33.3

solving for di2

di2 = - 10.3 cm

the final image is -10.3 cm

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

m = ( 66.7/40) * ( - 10.3 /33.3)

m = - 0.52