Question

Two concave lenses, each with f = -11 cm , are separated by 4.9 cm . An object is placed 24 cm in front of one of the lenses.

Find the location of the final image produced by this lens combination (in font of the lens closest to the object).

Find the magnification of the final image produced by this lens combination.

Answer 1

here,

focal length of each lens , f = - 11 cm

for first lens ,

the object distance , do1 = - 24 cm

let the image distance be di1

using the lens formula

1/f = 1/di1 - 1/do1

1/(-11) = 1/di1 - 1/(-24)

solving for di1

di1 = - 7.54 cm

for the second lens

the object distance , do2 = - (4.9 - di1) = - 12.44 cm

let the image distance be di2

using the lens formula

1/f = 1/di2 - 1/do2

1/(-11) = 1/di2 - 1/(-12.44)

solving for di2

di2 = - 5.84 cm

the location of the final image produced by this lens combination , di = 24 + di2 = 18.2 cm

the magnification of the final image produced by this lens combination , m = ( di1/do1) * ( di2 /do2)

m = ( - 7.54/(-24)) * ( - 5.84 /(-12.44))

m = 0.15