3. Find the position of the final image formed by the lens combination given in the following figure. 5+10+10] f-+10,-10 + 30 cm 30 cm -5+-1 0 cm cim Solution here, for the first lens the object distance , do1 = 30 cm focal length , f1 = 10 cm let the image distance be di1 using the lens formula 1/f1 = 1/di1 + 1/do1 1/10 = 1/di1 + 1/30 solving for di1 di1 = 15 cm for the seccond lens the object distance , do2 = 5 - 15 = - 10 cm focal length , f2 = - 10 cm let the image distance be di2 using the lens formula 1/f2 = 1/di2 + 1/do2 - 1/10 = 1/di2 - 1/10 solving for di2 di2 = infinite for the third lens the object distance , do3 = infinite focal length , f3 = 30 cm let the image distance be di3 using the lens formula 1/f3 = 1/di3 + 1/do3 1/30 = 1/di2 + 1/infinite solving for di3 di3 = 30 cm the final image is formed 30 cm to the right of third lens .

1. 3. Find the position of the final image formed by the lens combination given in the following
figure. 5+10+10] f-+10,-10 + 30 cm 30 cm -5+-1 0 cm cim
Solution
here,
for the first lens
the object distance , do1 = 30 cm
focal length , f1 = 10 cm
let the image distance be di1
using the lens formula
1/f1 = 1/di1 + 1/do1
1/10 = 1/di1 + 1/30
solving for di1
di1 = 15 cm
for the seccond lens
the object distance , do2 = 5 - 15 = - 10 cm
focal length , f2 = - 10 cm
let the image distance be di2
using the lens formula
1/f2 = 1/di2 + 1/do2

2. - 1/10 = 1/di2 - 1/10
solving for di2
di2 = infinite
for the third lens
the object distance , do3 = infinite
focal length , f3 = 30 cm
let the image distance be di3
using the lens formula
1/f3 = 1/di3 + 1/do3
1/30 = 1/di2 + 1/infinite
solving for di3
di3 = 30 cm
the final image is formed 30 cm to the right of third lens