Question

1. Two converging lenses with focal lengths of 40 cm and 19 cm are 10 cm apart. A 3.2 cm tall object is 15 cm in front of the 40 cm focal-length lens. Calculate the distance between the final image and the 19 cm focal-length lens and the final image height.

Answer 1

here,

for the first lens

the focal length , f1 = 40 cm

the object distance , do1 = - 15 cm

let the image distance be di1

using the lens formula

1/f1 = 1/di1 - 1/do1

1/40 = 1/di1 - 1/(-15)

solving for di1

di1 = - 24 cm

for the second lens

the focal length , f2 = 19 cm

the object distance , do2 = - 24 - 10 cm = - 34 cm

let the image distance be di2

using the lens formula

1/f2 = 1/di2 - 1/do2

1/19 = 1/di2 - 1/(-34)

solving for di2

di2 = 43.1 cm

the final image is 43.1 cm from the second lens

the object height , ho = 3.2 cm

the image height , hi = ho * ( di1 /do1) * ( di2 /do2)

hi = 3.2 * (-24 /-15) * ( 43.1 /(-34)) cm

hi = - 6.49 cm